Dynamic syntactic affinity group formation in a high-dimensional functional information system

ABSTRACT

The invention includes methods for algorithmically modifying a representation of a functional system based on functional trajectory signals by electronically representing a systems syntax, wherein the systems syntax comprises a logical data model, electronically constructing a representation of the functional system comprising a graph, based on an input signal algorithmically computing a functional trajectory that assesses magnitude, distance, or paths among at least two nodes, and updating the functional trajectory representing a set of paths through functional locations over time.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of application Ser. No.16/828,471, filed Mar. 24, 2020, which is a continuation of applicationSer. No. 16/541,303, filed Aug. 15, 2019, now U.S. Pat. No. 10,599,623,which is a continuation-in-part of application Ser. No. 16/000,519,filed Jun. 5, 2018, now U.S. Pat. No. 10,402,379, which is acontinuation of application Ser. No. 15/488,433, filed Apr. 14, 2017,now U.S. Pat. No. 9,990,380, which claims the benefit of U.S,Provisional Application No. 62/322,740, filed Apr. 14, 2016. applicationSer. No. 15/488,433 is a continuation-in-part of application Ser. No.14/967,313, filed Dec. 13, 2015, now U.S. Pat. No. 9,910,910 which is acontinuation of application Ser. No. 14/802,543, filed Jul. 17, 2015,now U.S. Pat. No. 9,361,358, which is a continuation of application Ser.No. 14/604,272, filed Jan. 23, 2015, now U.S. Pat. No. 9,098,564, whichis a divisional of application Ser. No. 14/216,936, filed Mar. 17, 2014,now U.S. Pat. No. 8,990,268, which claims the benefit of U.S.Provisional Application No. 61/802,245, filed Mar. 15, 2013, and U.S.Provisional Application No. 61/801,959, filed Mar. 15, 2013. Thisapplication also claims the benefit of U.S. Provisional Application No.62/887,091 filed Aug. 15, 2019, The contents of all of which are hereinincorporated by reference in their entirety.

FIELD OF THE INVENTION

The invention relates to an algorithmic method for dynamically combiningelements based on complex representations of an underlying functionalsystem.

BACKGROUND OF THE INVENTION

The analysis of complex systems, including the search and navigation oflarge data sets associated with, for example, biological, chemical,mechanical, physical, political, and economic systems, is challengingwithout an underlying functional model. Representations of these systemsand their constituent subsystems frequently have been derivedinductively or in an ad hoc fashion, and often are irreconcilable withone another.

The lack of ontological consistency, expressiveness, andinteroperability of these representations inhibits the capacity tocharacterize phenomena associated with complex systems, to predict theirbehavior accurately, to develop normative models of their outcomes, andto search complex functional data.

In existing search and navigation systems, search results are displayedas independent categories; any successive iteration utilizes metricsgathered through user-generated search and browsing history as well asad hoc content categorization systems derived from observation ofphenomena.

When data is organized in coordinate format geographically ortemporally, it is significantly easier to use for the purposes of query,navigation, and action. Other data management domains lack prior artmethods for establishing such an underlying standardized coordinatemodel. Applications and search tools derived from prior art methods arefrequently most effective when applied towards short-term individualizedrequests with clear geographic and temporal aspects, such as restaurantdelivery, current celebrity information, and taxi retrieval services.For substantive issues related to complex systems, such asenvironmental, economic, and political systems, the lack of a structuredsyntax for organizing the underlying qualitative information leavesassociated search and recommendation systems vulnerable tomisinformation and provides little to no mechanism for users to engineerand improve the underlying systems or understand relationships betweenthe parts and the whole.

Current machine learning techniques that seek to model phenomenaregarding complex systems frequently suffer from the curse ofdimensionality, a result of a nonsystematic approach to generating arepresentative space in which there is frequently no reason ex ante forany relationships among dimensions and correlations among them arelikely to be random.

A machine learning application usually begins by asking a question. As ageneralized example, one might want to classify a group of data into aset of groups, such as categorizing the content of a video throughdescriptive tags, and determining whether a patient has a disease givenparticular test results or is exposed to a health risk given a set oftest results. Often in these classification use cases, the categories towhich the applications are predicting do not have any a priori proximityrelationship with each other. As a result, when comparing predictionresults from such tests, machine learning applications that rely onerror-prone classification systems can fall short. In such cases, whileone can identify which data were classified incorrectly and theconfidence of the prediction, it is impossible to tell the machine howfar off the classification was, only that it was wrong. The predictionsand evaluations of predictions lack adequate notions of proximity in theoutputs and the assessments of those outputs.

The techniques are often highly opaque even to those who design,implement, and use them, often rendering it virtually impossible toaudit or verify their results until they have already impacted theunderlying system. The techniques also generally require extremely largedata sets to attain an acceptable level of accuracy, which tends todecline significantly when phenomena in a test set diverge even modestlyfrom those of a training set, a common challenge when dealing withinformation about complex systems.

BRIEF SUMMARY OF THE INVENTION

According to an embodiment of the invention for a method for modifying arepresentation of a functional system based on functional trajectorysignals, the method includes electronically representing a systemssyntax, wherein the systems syntax comprises a logical data model thatcan be applied by a computer processor to evaluate or generateexpressions of elements, wherein the elements represent parts,processes, and interactions of a functional system; electronicallyreceiving an input signal from a computing device, wherein the signalrepresents a functional attribute of an element, and storing the inputas an attribute of a data entity at a functional location, wherein thedata entity characterizes one or more of the elements; electronicallyconstructing a representation of the functional system comprising agraph U by assigning at a set of nodes N and a set of edges E connectedto N to model the functional system at time t₁, wherein N represents theinputs or outputs and E represents the transformations from inputs tooutputs; based on the input signal, algorithmically computing afunctional trajectory that assesses magnitude, distance, or paths amongat least two nodes n₁, n₂ from the set of nodes N to infer an outcome inthe functional system; constructing in G at least one new edgerepresenting a candidate new transformation E′ of components from inputsto outputs in the functional system based on the computed functionaltrajectory; electronically sending a functional message regarding E′ toa component of the functional system; updating the representation of thefunctional system to implement the candidate new transformation, thefunctional trajectory representing a set of paths through functionallocations over time.

According to some further embodiments, the input signal is capable ofbeing represented as a functional location in n-dimensional space, andwherein at least one of the dimensions in the n-dimensional spacerepresents a functional domain, the functional domain comprisingattributes of roles, order, or relationships among the elements; andfurther comprising: electronically assigning a set of functionallocations in the n -dimensional space to the data entity, the locationsbased on attributes of the data entity; and using the relationship ofthe data entity to reference points in the n-dimensional space over timeor movement of the data entity with respect to the reference points asan input to algorithmically computing the functional trajectory.

According to some further embodiments, the method includesalgorithmically using the functional locations in n-dimensional spaceand the graph representation derived from a systems syntax forpredicting changes in composition, structure or location of dataentities in n+k-dimensional space or the graph G; algorithmicallycomputing a functional velocity of the data entity based on ameasurement of a change of the composition, structure or locationrelative to positions or the reference points at two or more points intime; and algorithmically computing a predictive functional composition,structure or location of one or more of the elements in the underlyingsystem as represented by the data entity in the n-dimensional space at aset of specified future times, based on the computed functionaltrajectory and functional velocity.

According to some further embodiments, the method includeselectronically assigning at a set of nodes N′ and a set of edges E″ tomodel the functional system at time t₂ ; algorithmically deriving ametric regarding the evolution of one or more components of thefunctional system based on changes in the graphs from t₁ to t₂; andusing the metric to extrapolate or interpolate data regarding thefunctional system at time t₃.

According to some further embodiments, the method includes applying afunctional ranking algorithm to the graph, wherein the functionalranking algorithm assigns a score to a plurality of the components of Gby recursively calculating one or more strengths of the edges andassigning properties relating to functional attributes of the edges tothe connected nodes; and using the functional ranking algorithm torecommend a candidate new transformation E′″ a user.

According to some further embodiments, the method includes using {n₁,n₂,} ^e as inputs to a computational generative model to algorithmicallyconstruct a set of affinity groups A; simulating the performance of aplurality of affinity groups a_(1,2 . . . n) εA; applying adiscriminative model to rank the affinity groups; and modifying theranking based on a parameter related to the user.

According to some further embodiments, the method includes identifying asubset C′=c_(1 . . . n−k), k≥1 of the components that are located nearthe additional component c_(n+1) in G by using a functional vicinityalgorithm, wherein the functional vicinity algorithm returns a set ofcomponents within a threshold distance score in G based on a distancealgorithm; and engineering an interaction between the additionalcomponent and a component within the subset.

According to some further embodiments, the representation of thefunctional system is associated with a communication system, furthercomprising routing a plurality of the functional messages based onsimilarity of components within the functional system to direct thefunctional messages to one or more users of the functional system.

According to some further embodiments, the method includes modifying thefunctional system based on feedback received from the user; providing aplurality of search, recommendation, navigation, analytical, data feed,transaction, network, or security modules to a user based on thefunctional trajectory.

According to some further embodiments, the method includes constructinga community or group of functional members comprising a subgraph g ε G,wherein g comprises n₁, n₂ εN ^ e₁ε E; wherein the community or group isconstructed using a functional ranking algorithm applied to the subgraphg, wherein the functional ranking algorithm assigns a score to aplurality of the components of g by recursively calculating one or morestrengths of the edges and assigning properties relating to functionalattributes of the edges to the connected nodes; and wherein thefunctional community or group represents a plurality of elements sharinga plurality of the functional attributes; wherein n₁^n₂ represent users;and directing messages to community or group members represented by aplurality of the nodes based on the strength of edges in the subgraphconnecting the community or group members.

According to some further embodiments, a subset of G represents ageographic region, biological system, or grouping of functionalassignments, the functional trajectory represents a developmental pathfor the geographic region, biological system, or grouping of functionalassignments; and the functional velocity correlates to a growth rate,further comprising: taking the derivative of the functional velocity oneor more times to derive a higher-order derivative of the functionaltrajectory, and using the higher-order derivative to extrapolate orinterpolate a metric or outcome in the functional system; and using thevelocity or higher-order derivative as an input to computing thecandidate new transformation.

According to some further embodiments, the functional ranking algorithmis an input to an algorithm assessing affinity among users, furthercomprising: applying an algorithm to assess the diversity of affinitygroups and corresponding robustness or resilience to events; applying asimulator tool to assess potential modifications to the system and thelikely response of the group; and applying a technique selected fromamong agent-based modeling and systems dynamics modeling to determineprobabilistically varied time-series paths that may occur within a groupor in the larger system.

According to some further embodiments, the method includes usingmassively parallel processing to simulate the functional trajectory byassigning the set of inputs and outputs to computing devices and the setof edges to interactions among the computing devices; constructing afirst coordinate space C of dimensionality k: k>5 by assigning a set ofcoordinate values to the set of syntactic tags, wherein the distanceamongst the coordinate values in a plurality of dimensions correspondsto the similarity of attributes in the functional system; electronicallyinputting data regarding proportions and outcomes in the functionalsystem; and electronically assigning an order to the plurality ofdimensions based on the extent of predictive capacity of similarities ofcoordinate values for similarities of the outcomes in the functionalsystem.

According to some further embodiments, the method includesalgorithmically constructing a second coordinate space C′ by reducingthe dimensionality of the coordinate space C to k−x, x≥1, by selecting asubset of the plurality of the dimensions based on the order;electronically providing a set of visual representations of proportionsof the subset to a user; and comparing the set of visual representationsto diagnose a phenomenon in the functional system; wherein reducing thedimensionality decreases the computational search space, enabling theset of visual representations to be algorithmically provided to a userbased on express or implied preferences.

According to some further embodiments, N+E₁>10,000, and wherein a set oflocations in S are assigned based on a word embedding algorithm inhyperdimensional space of dimension d so that semantic meanings arerendered as tensors or vectors, further comprising: constructing atensor space or vector space of dimension 1≤d+t+s based on the output ofthe word embedding algorithm, temporal data in dimension t, andgeographic data in dimension s; assigning a set of functional markers toa plurality of the elements {g_(1,2 . . . n)} εG; wherein the functionalmarkers are selected from a semantic, visual, auditory or audiovisualtag applied to a set of functional data, and the functional markersassociate functional data, relationships, and a signifier; wherein theidentification of functional markers enables the provision of aninterface to a set of users to access search, recommendation, ornavigation results; assigning a rank to a plurality of functionalmessages based on their algorithmic distance in l or the similarity oftheir functional markers; and sending the functional message to a userbased on the rank and the properties of the user.

According to some further embodiments, the functional system isbiological or genetic; and the candidate transformation representsagricultural trait modification and intervening in the system comprisesusing precision gene editing to increase crop yields, diseaseresistance, or weather resistance.

According to some further embodiments, the functional system iseconomic, financial, monetary, or fiscal, further comprising:algorithmically simulating a plurality of outcomes related to thecomputed functional trajectories; and ranking the plurality of outcomesand associating the ranked outcomes with candidate new transformations.

According to some further embodiments, the method includes taking theintegral of the functional trajectory to determine the functional area;and using the functional area to inform the selection of the candidatenew transformation.

According to some further embodiments, the method includesalgorithmically identifying unique phenotypes to the elements based onfunctional locations and levels of expressions; computing a set ofmetrics and outcomes associated with unique phenotypes; and using uniquephenotypes to recombine, synthesize, or reengineer the elements toimprove outcomes in the functional system.

According to some further embodiments, the method includes storing acomputerized representation of a system S with elements E={e_(i)}, i=1,2. . . n, wherein S is comprised of subsystems s_(1,2 . . . j), with eachs_(i) having a set of elements ϑ₁ ⊂ E,

${{\overset{k}{\bigcup\limits_{1}}ɛ_{i}} = E},$wherein each e_(i) has characteristic properties p_(1,2 . . . i),

${{\overset{l}{\bigcup\limits_{1}}p_{i}} = P},$related to its inputs, outputs, or operations in S; constructing a setof expressions X={x_(i)}, wherein each x_(i) is comprised of acombination of two or more elements ε_(i) sharing a property p_(i),∃s_(i): x_(i) ⊃s_(i)∀x_(i)∈X; storing a population Z with data entitiesD={d₁}, wherein Z is comprised of subpopulations z_(1,2 . . . j), witheach z_(j) having a set of data entities Δ⊂D,

${{\underset{1}{\bigcup\limits^{k}}\Delta_{i}} = D},$with attributes A; wherein the collection of subpopulationsx_(1,2 . . . j) determines the structure of Z; constructing a set ofcomposites C={c_(i)}, wherein each c_(i) is comprised of a combinationof two or more data entities Δ_(i) sharing an attribute a_(i), ∃z_(i):c_(i) ⊃z_(i)∀z_(i)∈Z; and enabling a data creating, reading, updating,and deleting operation on the data entities.

According to some further embodiments, the method includes associating aset of numerical values V={v_(i)} with two or more subpopulations z_(i)and two or more composites c_(i); associating a set of statisticalproperties W={w_(i)} among z_(i) and c_(i); ordering z_(i) and c_(i)such that w_(c)>w_(z).

According to some further embodiments, f: S→Z, g: E→D, and h: P→A aresurjective; and e: X→C is surjective.

According to an embodiment of the invention for a system for enabling amodification of a functional system based on a computation of functionaltrajectory, the system includes an electronic representation of asystems syntax, wherein the systems syntax comprises a logical datamodel that can be applied by a computer processor to evaluate orgenerate expressions of elements, wherein the elements represent parts,processes, and interactions of an underlying system; an electronic inputfrom a computing device, wherein the data entities at a functionallocation characterize one or more of the elements, and storing the inputas a data entity; a graph G comprising a set of nodes N and a set ofedges E assigned to model the functional system at time t₁, wherein Nrepresents the inputs or outputs and E represents the transformationsfrom inputs to outputs; an algorithmic computation of functionaltrajectory that assesses magnitude, distance, or paths among at leasttwo nodes n₁, n₂ from the set of nodes N to infer an outcome in thefunctional system; an output of computing the functional trajectory toinform the electronic construction in G; at least one new edgerepresenting a candidate new transformation E′ of components from inputsto outputs in the functional system; a signal regarding E′ sent to acomponent of the functional system; an update in the representation ofthe functional system to implement the candidate new transformation, thetrajectory representing a set of paths through functional locations overtime across the universe of elements E.

According to some further embodiments, the system includes a collectionof subsystems {s_(j)}⊂P (E), wherein every element is in at least onesubsystem; a universe of properties P; and a function for associatingelements with properties f: E→P(P), wherein the function is surjective.

According to some further embodiments, a plurality of N represents laborin the functional system and the signal indicates potential jobtraining, skill development, job application, recruiting, job placement,hiring, staffing, promotions, or labor policy, further comprising: aninclusion function for associating subsystems comprising members of{s_(j)} with their elements such that f: {s_(j)}→E; wherein Z comprises:a universe of data entities D; a collection of subpopulations{z_(j)}⊂P(D); a universe of attributes A; a function for associatingdata entities with attributes g: D→P(A) a map carrying; {s_(j)}↔{z_(j)},P↔A; a simulation function assigning a probability distribution K to aset of outcomes associated with a plurality of z_(j); and a map φ: D→Ethat associates a set of data entities with a set of elements of thesystem.

According to some further embodiments, the system includes an electronicset of nodes N′, and a set of edges E″ that model the functional systemat time t₂; an algorithmically derived metric regarding the evolution ofone or more components of the functional system based on changes in thegraphs from t₁ to t₂; and an extrapolation or interpolation of databased on the algorithmically derived metric regarding the functionalsystem at time t₃.

According to some further embodiments, the system includes a functionalranking algorithm applied to the graph, wherein the functional rankingalgorithm assigns a score to a plurality of the components of G byrecursively assessing the strength of the edges and imputing certainproperties of the edges to the nodes they connect; and a recommendationto a user of a candidate new transformation E″ based on the functionaltransformation.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an overview of an example method.

FIG. 2 illustrates an example logical data model.

FIG. 3 illustrates an example ordered set of fields showing examplerelationships among fields.

FIG. 4 illustrates an example tagging and dimensional representation ofdata entities.

FIG. 5 illustrates an example method for characterizing vicinities andinferring properties.

FIG. 6 illustrates an example of a defined vicinity comprising referenceentities.

FIG. 7 illustrates an example representation of vicinities defined inthree-dimensional functional space.

DETAILED DESCRIPTION OF THE INVENTION

In the following description of embodiments, reference is made to theaccompanying drawings that form a part hereof, and which show by way ofillustration specific embodiments of the claimed subject matter. It isto be understood that other embodiments can be used and that changes oralterations, such as structural changes, can be made.

Such embodiments, changes, or alterations are not necessarily departuresfrom the scope with respect to the intended claimed subject matter.While the steps below can be presented in a certain order, in some casesthe ordering can be changed so that certain inputs are provided atdifferent times or in a different order without changing the function ofthe systems and methods described.

The procedures described below could also be executed in differentorders. Additionally, various steps that are described below need not beperformed in the order disclosed, and other embodiments usingalternative orderings of the steps could be readily implemented. Inaddition to being reordered, the steps could be decomposed intosub-computations.

As characterized herein, a user can take any form, such as anindividual, organization, computerized process such as a bot orautomated process. As used herein, variable names may be repeated indifferent sections, although not necessarily referring to the same namedreferent elsewhere.

In some embodiments, a language is constructed or selected. Asnon-limiting examples, the language can be formal, symbolic, artificial,controlled, natural, or some combination thereof.

Functional Information

In some embodiments, a transformation t can be defined as a processconverting a set I of input elements to a set O of output elements.Functional systems comprise a set T of transformations, sets I and O, aswell as the requisite bodies and phenomena that catalyze, facilitate,and accomplish those processes.

A functional system can be modeled as logically structured informationassociated with transformations or input-output processes comprising aset of elements, as well as associated entities, processes,relationships, and their attributes and values. In natural language,these can correspond to lexical categories of nouns, verbs, adpositionsand conjunctions, adjectives and adverbs, and numbers. In someembodiments, symbols can be assigned to the elements and organized inaccordance with an order in the underlying functional system. Thesymbols can characterize elements that can be derived from morefundamental assumptions. The identification of these assumptions canfacilitate the synthesis of methods for characterizing the functionalsystem, enhancing the connectivity of elements, the management ofexposures, and the flexibility of models across domains.

In some embodiments, function can be unified with other propertiesalready easily rendered in coordinate space, including, as non-limitingexamples, space, time, color, sound, light, current, and heat, as wellas measures of information and value, enabling visual, aural, andspatial expression and transmission of functional information acrossdomains, for applications including, but not limited to, search andnavigation of information about complex systems.

As a non-limiting example, color can be assigned a set of lexical unitscorresponding to its order on the spectrum. In some embodiments,proximate colors can equate to proximate functions. As non-limitingexamples, colors can comprise sequential markers, relational tags,relational coordinates, sequential values with a point of reference,syntactic coordinates, or a representation of a functional syntax.

In some embodiments, the combination of symbols representing functionalinformation constitutes an expression, which can be represented by ametatag. A syntax can be constructed which enables the evaluation of thevalidity of expressions as well as the generation of new expressions.

Syntactic tags can be assigned in a database to symbols and fields inexpressions as well as to underlying elements of the functional system,enabling applications in search, retrieval, visualization,recommendation systems, and descriptive and predictive analytics, aswell as facilitating and enabling interactions among elements of thefunctional system. Functional information can be associated with dataentities representing elements of the underlying functional system usinga logical data model, as described below.

FIG. 1 illustrates an overview of an example method according to theinvention. The method can include representing data entities in adatabase system (105), the database system comprising a logical datamodel for structuring data sets (110), the logical data model comprisesat least two fields ordered by a set of interrelationships among atleast two elements in the underlying functional system (115) or forstructuring data sets from which functional information can be derived(116), the functional information system defines reference points in ann-dimensional space for the data entities (117) or data for whichfunctional referents can be assigned, and associated nonfunctional dataaccording to the set of interrelationships (118), selecting a type offunctional proximity and an algorithm based on the type (120),functional proximity measures correspondence among a set of referencepoints, and a functional proximity algorithm defines executable stepsfor computation of the correspondence based on the magnitude ofrelationships among a plurality of the data entities (125), andexecuting the functional proximity algorithm on a data set comprising asubset of the data entities in the database to generate a set offunctional proximity results (130) or executing a set of steps thattakes as input a set of characteristics and returns as output a set oflocations in n-dimensional functional space (135).

Logical Data Models and Syntactic Unification in Functional InformationSystems

A logical data model can be defined for functional information thatspecifies the elements of the underlying functional system and theirinterrelationships. In some embodiments, the logical data can compriseat least two fields ordered by a set of interrelationships among atleast two elements in the underlying system, wherein theinterrelationships correspond to the functional properties of a processconverting a set of input elements into a set of output elements. Insome embodiments, the logical data model can be represented in acomputing environment as a layer of operations on a database offunctional information in the form of a functional information system.

The structure of a functional information system can be designed toreflect the underlying relationships present in the referent orunderlying functional system in order to improve a user's capacity tosearch, index, discover, and create functional and non-functionalinformation. In certain embodiments, the logical data model, or subsetsthereof, can be used to create feature sets for machine learningtechniques, as described further below.

In some embodiments, functional information is tagged and organizedusing a standardized set of fields which can provide units for one ormore functions represented in n-dimensional functional space. Thestandardized set of fields can be discrete or continuous. Oncestructured, functional information can be associated with other types ofinformation organized by analogous systems of interval measurement,including, as non-limiting examples, standardized systems for measuringand representing geographic and temporal information.

FIG. 2 illustrates an example logical data model according to theinvention. The logical data model comprises ordered fields (205C, 210C,215C) defined by underlying interrelationships among real-world systems.Classes may be subclasses of other classes, for example, if onerepresents the sub-systems of another. Between levels of classes,relationships between fields are captured as well. Arrows between 205C,210C, and 215C represent correspondences between fields in each layer,dotted lines show identity. 205A, 210A, and 215A illustrate the dataentities of classes 205C, 210C, and 215C, respectively. Fields set 205C,element “1” is functionally proximate to Fields set 210C, element “1”,which correspondence is also illustrated between 205A and 210A.

FIG. 3 illustrates an example ordered set of fields showing examplerelationships between the fields according to the invention. Field 305(“1”) is a defining association of Field 310 (“1”), which jointlydescribe an action performed upon an object described in Field 315(“C”). Fields 320 and 325 (“1” and “2” respectively) describe asequential step of the action described in Fields 305 and 310, anddescribe an action performed upon an object described in Field 330(“C”). Field 335 (“1”) is a sequential step of Field 320 (“1”), and is adefining association of Field 340 (“3”), which jointly describe anaction performed upon an object described in Field 345 (“B”). Asdiscussed herein, a functional proximity algorithm can be configured tocompute correspondence based on the magnitude and category ofrelationships among a plurality of the data entities, such as thatbetween Field 325 and Field 315, or Field 325 and Field 305.

FIG. 4 illustrates an example tagging and dimensional representation ofdata entities. As illustrated, data entities A and B (405) arerepresented in a logical data model (410), functionally tagged (415),and stored with a distance d that has been calculated (425). Asdiscussed herein, the distance calculation may be made based on themagnitude and category of relationships among a plurality of the dataentities. As illustrated, the entities “A” and “B” can be represented inthree-dimensional functional space (420), having functional distance “d”

Logical Data Model Unification

Without loss of generality, the unification of, as non-limitingexamples, vectors, codes, strings, sequences, or tensors using thesestructures can be represented, in certain embodiments, as {x₁₁,x_(in)}∪{y₁₁, y_(ln)}→{x₁₁′ . . . x_(ln)′, y₁₁′ . . . y_(ln)′}. This canbe extended to the unification of matrices and to the unification of anarbitrary number of arbitrary large or disparate sets of, asnon-limiting examples, vectors, codes strings, sequences, or tensors. Incertain embodiments, the methodologies described herein can facilitatethe representation of this data in a graph format in which a subset ofthe matrix corresponds to nodes and another subset corresponds to edges.As a non-limiting example, the resultant interoperability and reductionin surface area of the space can increase the speed of computation, asdetermined by a test of statistical significance.

Associating functional information that is structured to reflectinterrelationships among elements with information from other domainsthat is also structured to reflect interrelationships among elementsprovides users enhanced search and navigation capabilities by enablingcross-comparative reorientation and pivot functionalities and increasesthe granularity in architectural indexing and search functionalities.Standardizing the representation of functional systems in a naturalspace facilitates applications that utilize the representation to find,relate, and create information about sub- and super-systems relative tothe original referent functional system. The unification of structuredinformation that reflects interrelationships across domains andunstructured information can facilitate composite views of the dataincluding, as a non-limiting example, through computer-mediatedsimulations.

Set Theoretical Representation of Logical Data Model Fields

Loci can be constructed by combining tags or metatags; as a non-limitingexample, a locus can comprise the tuple (α,γ,λ,r,s,v). In otherembodiments, a locus can comprise the tuple (α, γ, r, s). In otherembodiments, a locus can comprise the tuple (r₁, s₁, v₁, α, γ, λ, r₂,s₂, v₂). In other embodiments, there can be no inherent order within alocus.

In some embodiments, when the system is functional, inputs, outputs, andfunctions can be modeled as(α,γ)(r₁, s₁)→(r₂, s₂)

In other embodiments, which include substaging, the inputs, outputs, andfunctions can be modeled as(α, γ, λ)(r₁, s₁, v₁)→(r₂, s₂, v₂).

A field or level can be comprised of one or more loci; in someembodiments, the loci comprising a field or level can be ordered byproximity relative to a reference point. As non-limiting examples, theproximity can be functional, morphological, physiological, anatomical,physical, semantic, temporal, lexical, geographic, positional,syntactic, or some combination thereof. In some embodiments, the locican be ordered, in part or in whole, with respect to the proximity oftheir referents in the functional system.

As a non-limiting example, a field can characterize one or more nodes ina graphical representation of the functional system. In someembodiments, a barcode can comprise one or more fields. In someembodiments, the tags, functions, inputs, outputs elements, or locirepresented or included in a field, level, or barcode will be morehomogeneous than an arbitrarily large random sample from the database,as validated by a statistical test.

The lexical categories, tags, and metatags can be used, as non-limitingexamples, to construct data structures such as loci, fields, levels,barcodes, stratified or segmented lexical architectures, or somecombination thereof. In some embodiments, a first lexical category R,comprising lexical units r_(1,2 . . . n), is selected, and a pluralityof the lexical units are electronically tagged with lexical categorystages S=s_(1,2 . . . m), wherein Sε

(R). A second lexical category A, comprising lexical unitsa_(1, 2 . . . o), is selected, and a plurality of the lexical units areelectronically tagged with lexical category stages Γ=γ_(1,2 . . . p),wherein Γε

(A). In some embodiments, an arbitrary number of further lexicalcategories can be assigned,

In some embodiments, electronic tags or metatags representing lexicalcategory substages Y=v_(1,2 . . . q) are then assigned to a plurality oflexical units in S, wherein Yε

(S). Electronic tags or metatags representing lexical category substagesΛ=λ_(1,2 . . . v) are then assigned to a plurality of lexical units inΓ, wherein Λε

(Y). In some embodiments, an arbitrary number of further substages canbe assigned.

In some embodiments, the logical data model described herein maycorrespond to the lexical architecture. The logical data model can beused, in some embodiments, in conjunction with a syntax or systemsyntax, that can, as non-limiting examples, be applied by a computerprocessor to generate or evaluate linguistic expressions by iteratingthrough the database to relate or assess a plurality of lexicalcategories, category stages, lexical units, tags, or combinationsthereof. In some embodiments, the expressions can include loci thatfacilitate, as non-limiting examples, the temporal, spatial, mechanical,physical, biological, ecological, economic, financial, political,anatomical, morphological, or morphosyntactic modeling of the system.

In some embodiments, the logical data model can facilitate visualcomparative analytics by electronically iterating through the databaseto assign one or more colors, shapes, scales, or shades to a pluralityof lexical categories, category stages, or lexical units. In someembodiments the tags, expressions, lexical architectures, fields,levels, barcodes, or loci will facilitate computer-enabled modeling ofsystems with analytical tools that can be demonstrated to increasedescriptive, retrodictive, or predictive accuracy of the behavior ofsystems, subsystems, or elements using a test of statisticalsignificance.

Set Theoretical Representation of Expressions

In some embodiments, a computerized representation of a system S isstored comprising elements E={e₁, . . . e_(n)}, and a set of subsetsB={ε₁, . . . , ε_(n)} wherein each ε_(i) ⊂E, wherein a plurality of ε∈Bhave characteristic properties p_(i)∈P, with p_(i): B→A_(i), and theelements of A_(i) are related inputs, outputs, or operations of theε_(i)'s.

As a non-limiting example, a set of expressions X is constructed,wherein each x_(m) ∈X is comprised of a combination of two or moreelements ε_(i) sharing a property a_(i) ∈A_(i), such that ∀x_(i) ∈X,∃ε∈B such that ε_(i) is in x_(i).

A population Z can be stored with data entities D={d_(n)}, wherein Z iscomprised of subpopulations with each z_(1,2 . . . v), having a set ofdata entities Δ⊂D,

${{\underset{1}{\bigcup\limits^{k}}\Delta_{o}} = D},$with attributes A. As non-limiting examples, f: S→Z, g: E→D, and h: P→Acan be bijective, injective, or neither. The collection ofsubpopulations z_(1,2 . . . v) can determine the structure of Z.

In some embodiments, a set of composites C can be constructed, whereineach c_(u) ∈C is comprised of a combination of two or more data entitiesΔ₀ sharing an attribute a_(w) ∈A_(i) for some i , ∃z_(v): c_(u) ⊃z_(v)∀z_(v) ∈Z. As non-limiting examples, e: X→C can be bijective, injective,or neither.

As a non-limiting example, a set of numerical or categorical values willbe associated with two or more subpopulations and two or morecomposites, which can be associated with a set of statisticalproperties, such as correlation or covariance. The subpopulations andcomposites will be ordered, as a non-limiting example, based on a set ofstatistical tests associated with the statistical properties andnumerical values.

Stratified or Segmented Lexical Architectures

The lexical categories and category stages can comprise, in someembodiments, a stratified lexical architecture. In some embodiments, thestratified lexical architecture will include substages. A subset of thestratified lexical architecture can comprise a segment in someembodiments. A segment can include, as a non-limiting example, a stageand two substages.

In some embodiments, a system comprises a set of elements, which can berepresented by a set of lexical units. In some embodiments, the systemwill be functional, wherein a functional system relates the elementsaccording to their roles in a process converting a set of input elementsto a set of output elements. In other embodiments, the system will bemechanical, morphological, physical, chemical, aeronautical, biological,ecological, anatomical, syntactic, morphological, morphosyntactic,linguistic, grammatical, political, socioeconomic, economic, financial,monetary, or fiscal.

As non-limiting examples, these lexical units can be representedsyntactically, morphologically, semantically, symbolically, formally,mathematically, aurally, visually, as morphemes, words, phrases,clauses, or some combination thereof.

In some embodiments, electronic tags or metatags representing lexicalcategories are assigned to the lexical units; as non-limiting examples,these tags or metatags can be semantic, syntactic, symbolic, written,visual, aural, tactile, or some combination thereof. As non-limitingexamples, the lexical categories can be nouns, verbs, adjectives,pronouns, adverbs, adpositions, or conjunctions.

A database representation of a stratified or segmented lexicalarchitecture, can, as a non-limiting example, enable a computerprocessor to cluster data entities based on their semantic, syntactic,or symbolic relationships.

Overview: Locations in a Logical Data Model

A functional system has a set of functional locations in the underlyingsystem as well as its representation in graph and coordinate space, asdescribed further below. Functional location or region have, asnon-limiting examples, relative positions; associated qualitativeproperties, and associated quantitative properties, which may befunctional or non-functional. A computer can match a location withinformation associated with a specific location. A computer can also useinformation in a functional information system associated with a dataentity to assign a functional location to the specific functional dataentity.

The identification and assignment of locations enables the calculationof functional proximities, which indicate, as non-limiting examples, thesimilarity among the locations and the magnitude of relationships amongthe elements and their representations. The capacity to determinefunctional proximity enables the definition of functional regions orvicinities around a reference point in functional space. Functionallocations relative to any given location and functional proximities canbe determined using a functional proximity algorithm, described below.This algorithm can, as non-limiting examples, determine relativedistances, and associate relative qualitative and quantitativecharacteristics.

FIG. 5 illustrates an example method for characterizing vicinities andinferring properties according to the invention. Given entities A and Bwithin a vicinity V, each are known to bear the property P1. Entitieswithin vicinity V bear property P1, and thus property P1 is associatedto vicinity V. Entity C, which is within vicinity V, is not known tohave or not have property P1. Through C's membership in V, the propertyP1 can be inferred for entity C. Given entity D which bears property P1,has not yet been located within functional space. By examining thisproperty against the properties of the vicinity V, entity D's locationmay be inferred to be in vicinity V.

FIG. 6 illustrates an example of a defined vicinity (605), comprisingreference entities α, β, and ξ, as a representation of a vicinity inthree-dimensional functional space. Vicinity 605 can comprise anarbitrary number of vicinities.

FIG. 7 illustrates an example representation of vicinities defined inthree-dimensional functional space. As illustrated, each vicinity 705,710, and 715 can comprise an arbitrary number of entities. Vicinitiesmay be overlapping (705 and 710), non-overlapping (705 and 715), orwholly bounded within other vicinities (as 715 is bounded within 710).

Coordinate Representations

The capacity of a logical data model to syntactically integraterepresentations of functional systems facilitates computation in anarbitrary number of dimensions that preserve the structure of theunderlying functional system and which can be verified through a test ofstatistical significance. As a non-limiting example, the symbols can berepresented as variables, which can be discrete or continuous. As anon-limiting example, each symbol can be mapped in a dimension incoordinate space, specifically a functional coordinate space, with thedimension characterizing any subset of the underlying functional system,In some embodiments, the coordinates can be projected down to a lowerlevel of dimensionality, or a subset of coordinate space can beselected, and can be represented in a grid. The coordinates can berepresented in an arbitrary number of dimensions. Positions can be fixedor changing in some or all dimensions.

When the subset of the underlying functional system mapped in adimension is cyclical, polar coordinates can be analytically useful. Inother embodiments, other orthogonal coordinate representations,including, as non-limiting examples, spherical, cylindrical, or affinerepresentations, can be beneficial, In other embodiments, non-orthogonalcoordinate systems and representations can be analytically useful.

Clustering and weighting algorithms can be used to increase thepredictability, normality, or stability of outcomes related to elementsof the functional system; the high-dimensional representations enabledby the methodology described herein can be particularly suited toachieving these objectives for large population sets.

Coordinate Representations: Natural Language-Independence

Coordinate-based tagging systems are natural language-independent, butindividual tags can be applied to select natural language terms that canbe associated with a specific coordinate-based location by fixing andstandardizing their semantic meaning. The interoperability of functionalcoordinates and natural language enable the system to link disparatetypes of information concerning complex systems. In some embodiments,users can fix any value of the coordinate system to a defined level ofgranularity and compare results by varying other values.

The interoperability of functional coordinates and natural languagefurther enables the system to predict or retrodict connections, links,or associations within and across functional systems based on one ormore associated links or connections. The capacity to fix values to anarbitrary or user-specified level of granularity can enable inter-levelpredictions or retrodictions by using one or more links, connections, orassociations on one level to predict or retrodict links, connections, orassociations on another level.

In some embodiments, divergent systems of non-functional data, includingas non-limiting examples legacy databases and categorical classificationsystems, may be assigned functional coordinates through a semantic andsyntactic association process.

N-Dimensional Representations

In certain embodiments, a representation of a functional system can berendered in an arbitrary number of dimensions. As a non-limitingexample, each element of a logical data model can be associated with adimension, wherein the dimension characterizes any subset of theunderlying functional system. In some embodiments, all dimensions have ameasurable relationship with all other dimensions, and are linearlyindependent; in other embodiments, some dimensions have a measurablerelationship with some other dimensions, and are linearly dependent. Insome embodiments, a single dimension may be used to define a referencepoint within n-dimensional space; in other embodiments, multipledimensions may be used. Dimensions with direction and value can comprisea vector subspace of the representation.

In some embodiments, unlocking the dimensionality of relations amongobjects in a functional system, aligning it with the inherentdimensionality of existing domain-specific representations as well ascoordinate and measurement systems organizing both functional andnon-functional information, and unifying the representation into asingle coordinate system can be used as an approach to unitingdomain-specific characterizations of elements, integrating syntacticdata management techniques, and improving ranking and scoring measures,thereby enhancing the modeling of systems as well as the computer-aideddesign and synthesis of subsystems. In some embodiments, certaindimensions may be selected as representative; in other embodiments, adimensionality reduction algorithm can be used for analytical purposes.As a non-limiting example, a representation of a functional system inn-dimensional space and sub-regions of the representation can be definedas a reference point and used as inputs to and outputs from functionalalgorithms.

Graph Representations

In certain embodiments, a representation of a logical data model may berendered graphically. As a non-limiting example, tags or metatagsderived from the logical data model can be associated with elements ofthe underlying functional system, the tags and metatags representingnodes and edges in the graph representation of the system. As anon-limiting example, data entities can be assigned nodes andinterrelationships can be assigned edges, while processes, attributes,and values can be assigned to either. In certain embodiments, sets ofnodes and edges can aggregate into individual nodes, while nodes can bedisaggregated into sets of nodes and edges.

As a non-limiting example, a set of lexical category stages or substagescan represent entities or processes whose sequence in the lexiconrepresents their order in the underlying system. In certain embodiments,these successive stages or substages can be assigned nodes. As anon-limiting example, a set of lexical category stages or substages, orlexical units can represent processes or relationships in the underlyingsystem, which can be assigned edges, as described further below.

In some embodiments, a graph can be presented to a user, as non-limitingexamples, with functional, syntactic, symbolic, coordinate, visual,aural, audiovisual, mathematical, linguistic, geographic, or temporalrepresentations of data, enabling the user, as non-limiting examples, tosort, store, retrieve, query, visualize, or analyze the system, or somecombination thereof. As a non-limiting example, a graphicalrepresentation of a functional system and sub-regions of therepresentation can be defined as a reference point and used as inputs toand outputs from functional algorithms.

In some embodiments, graph representations of functional systems can beprojected onto a set of coordinate planes, and analytics can be run onat least two graph representations that measure and compare the relativestructure and outcomes of the functional systems. The output ofcomparative analysis may be used, as non-limiting example, for aprognosis or diagnosis of the underlying functional systems; the outputsmay also be used to suggest changes to the underlying functional systemto achieve a normative or desired outcome.

In some embodiments, a set of tags or metatags can constitute a string.As non-limiting examples, a systems syntax can enable the generation orevaluation of combinations of strings. As a non-limiting example, thealgorithmic identification of string sequences can enable the generationof graphs of subsystems that can be connected at scale through thesyntax governing relationships. In some embodiments, a set of nodes oredges can be associated with a top-level domain for websitearchitecture, as described in more detail below.

Functional Algorithms

Using the methods described herein, qualitative, quantitative,functional, syntactic, and non-functional information can be associatedwith elements of a logical data model in a functional informationsystem. A functional system may be represented, as non-limitingexamples, using lexical architecture, set theoretical notation,coordinate systems, and n-dimensional and graph structures.

Functional algorithms can be used to locate and relate entities withinrepresentations of functional systems. As non-limiting examples,functional algorithms can be used to calculate or compute position,distance, space selection, vector, and closeness. In some embodiments,the computation of functional algorithms enables, as non-limitingexamples, enhanced storage, visualization, search, retrieval, andanalytical applications for large data sets associated with functionalsystems.

In representations of functional systems, there are, as non-limitingexamples, two classes of algorithms that are important in thefunctionality of the underlying information system: functionalpositioning algorithms and functional proximity algorithms. As anon-limiting example, a functional positioning algorithm represents theset of steps that take information inputs associated with an untaggeddata entity in order to identify and tag the data entity's functionallocation, thereby mapping it onto functional space. As a non-limitingexample, a functional proximity algorithm represents the set of stepsthat take a tagged data entity and its functional location, and providesa set of measures on its proximity to other functionally locatedentities within the system, thereby enabling the system to provideinformation on other entities functionally proximate to the entity.Analogs to these algorithms exist in geographic information systems. Thefirst, a geographic positioning system, represents a set of steps thattakes information inputs associated with an unlocated entity and usesthose inputs to identify and tag the entity's geographic location ,thereby mapping it onto geographic space. The second, a geographicproximity algorithm, represents the set of steps that take ageographically tagged data entity, and provides a set of measure on itsits proximity to other geographically located entities, thereby enablingthe system to provide information on other entities geographicallyproximate to the entity.

In databases containing functional system information, it is possible touse functional positioning algorithms to search and find functionallocations for elements by inputting qualitative or quantitativeinformation associated with the element.

In databases containing functional system information, it is possible touse the specific functional location of an element to find functionallyproximate elements and information using a functional proximityalgorithm, such as applications in proximity, vicinity, navigation, andtrajectory, as described below.

Functional Positioning Algorithms

In some embodiments, the discovery of the underlying order of afunctional system enables the functional system to be mapped and modeledwith greater precision and accuracy. A functional algorithm can beconstructed to place an entity within a coordinate representation of afunctional system.

As a non-limiting example, the discovery of the underlying properties ofan entity in the functional coordinate system enables derivation of anentity's location within that system through inference or machinelearning methods. As non-limiting examples, an entity's location infunctional coordinate space can be inferred from a variety ofinformation, such as its vicinity as described below, its functionalproximity to related entities as described below, its associatedsyntactic or non-functional information that can be correlated to thestructure or outcomes of previously defined entities within the system,and other information that can enhance flexibility, connectivity,control, precision, and descriptive and predictive accuracy for numerousapplications.

Graded Functional Proximity

As discussed herein, functional proximity indicates relative similarityof functional characteristics and relative location in an underlyingfunctional system. In certain embodiments, graded functional proximitymay reflect asymmetry of closeness or divergence of similarity byperspective among entities within an underlying functional system orfunctional information system, in which directional or empirical factorsmay influence calculations. As used herein, the term functionalproximity shall encompass graded functional proximity. In certainembodiments, functional proximity is a measure of relative closenessamong entities defined by a functional coordinate system in then-dimensional space among a plurality of reference points, In otherembodiments, functional proximity measures correspondence among a set ofreference points, and a functional proximity algorithm definesexecutable steps for computation of the correspondence based on themagnitude and category of relationships among a plurality of the dataentities.

As discussed herein, syntactic proximity indicates relative similarityof characteristics that are structured in the logical data modelaccording to their order in an underlying functional system. In someembodiments, there exists an intersection among the characteristicsassociated with functional proximity and syntactic proximity. In someembodiments, a variety of proximity algorithms, including, asnon-limiting examples, functional, non-functional, syntactic, andhybrid, can be computed and then assigned weights, facilitating adetermination of overall proximity. A hybrid proximity algorithm, asused herein, can be defined as a computation that delineates similarityof characteristics according to a combination of functional,non-functional, and/or syntactic proximity measures. As non-limitingexamples, a computer or user can select a set of proximity measures,weights, or scoring measures.

Functional Proximity: Coordinate Embodiments

Functional coordinates can provide sufficient information about dataentities in order to perform functional proximity calculations amongthem.

In some embodiments, a weighted average similarity scheme can be usedbetween sets of strings, tags, or metatags in which partial matches areconsidered. As non-limiting examples, the weights to be assigned toportions of the strings, tags, or metatags that can be compared can bepredetermined, specified by the system, specified by the user, or somecombination thereof.

In some embodiments, a categorical distance measure can be applied tosets of strings, tags, or metatags. As non-limiting examples, thestrings, tags, or metatags can be viewed as vectors or scalars, whilethe measure can be based on the frequency of attributes or values incomparable subsets of the strings, tags, or metatags as a proportion ofa whole population being studied. As a non-limiting example, for any twovectors or scalars of strings X, Y, with N entries in the vector, theirproximity or weight can be calculated as

${S = {\sum\limits_{k = 1}^{n}\;{\left( {{\delta\left( {X_{k},Y_{k}} \right)}\left( {1 - p_{x_{k}}^{2}} \right)} \right)/N}}},$in which each equation is weighted by the Kronecker Delta function. Insome embodiments, matches are only made if attribute X_(k) is equivalentto attribute Y_(k).

In other embodiments, a set of metrics can be associated with locationsin functional space. As non-limiting examples, the associated metricscan indicate the prevalence or probability of a given entity at a givenfunctional location; the metrics can be rendered, as non-limitingexamples, as vectors, tensors, matrices, arrays, metadata appended tographs or coordinate representations, or some combination thereof.

The data concerning functional locations can, in certain embodiments, becombined with, as non-limiting examples, temporal or geographic data tofacilitate comparative analytics. In embodiments including vector andtensor representations, distance algorithms can be applied to determinethe functional similarity among, as non-limiting examples, time periodsor geographic regions, which can enhance, as non-limiting examples,retrodictive and predictive analytics as well as search andrecommendation results.

Functional Proximity: Graph Embodiments

In some embodiments, proximity measures associated with a graphrepresentation of a functional system will enable the identification ofclusters centered around medoids, wherein a medoid is a representativepoint in a dataset that is most similar to other points in the set. As anon-limiting example, medoids can be generated through random walks,which can be simulated, or through a k-nearest neighbors algorithm.

In other embodiments, a structural functional proximity algorithm can beused. A graph-based algorithm will be defined that assesses similaritybetween data entities based on, as a non-limiting example, empiricalconnections within the underlying functional system. The graph-basedalgorithm can, in some embodiments, search for functionally similarreplacement nodes when the set of empirical connections representedwithin the functional information system may be incomplete. As anon-limiting example, functionally similar replacement nodes can beidentified through a different functional proximity algorithm.

Functional Proximity: Connectivity Embodiments

In some embodiments, proximity can be derived from the empiricalrelationships among the entities, which can be aggregated, stored, andassigned to data entities and their referents. These empiricalrelationships can be weighted, scored, timestamped, or geotagged, andstored in one or more databases as a basis for proximity calculations.In some embodiments, the proximity metrics can be overlaid with, asnon-limiting examples, geographic or temporal data for the purposes ofsearch, analysis, or visualization.

In some embodiments, a connectivity-based algorithm can be defined whichassesses the shortest path among nodes, repeatedly deletes edges, andrecalculates the shortest path after a plurality of deletions. In someembodiments, the connectivity-based algorithm will continue to deleteedges until there is only one path, and will compute a connectivityscore based on a composite score of shortest paths before and afterdeletions. In some embodiments, the connectivity score can be consideredas part of a proximity algorithm. In some embodiments, the connectivityscore can be considered as part of a proximity algorithm. In otherembodiments, a position algorithm can be defined which compares aplurality of in and out edges of a plurality of nodes.

Functional Proximity: Adapted Embodiments

As a non-limiting example, the Manhattan distance can be used to derivea functional proximity metric by comparing a set of locations inn-dimensional functional space. In some embodiments, the computerizedsystem will assign a score s₁ if the reference point locations arenearby, and a different score s₂ if the reference point locations aredistant.

In some embodiments, the measures of functional proximity can becombined with measures of proximity for numerical variables in the dataset. As non-limiting examples, these measures can be computed usingMahlanobis distance, covariance kernels, or Euclidean distance. In someembodiments, the distance can be calculated after dimension reductionassociated with, as a non-limiting example, principal componentanalysis.

As a non-limiting example, the proximity among clusters can bedetermined through Jaccard similarity, wherein the Jaccard similarity isthe intersection of the clusters divided by their union. In otherembodiments, transition probabilities in the random walk can enable adetermination of proximity; as a non-limiting example, this can bedetermined through a transition probability matrix.

In some embodiments, a stationary distribution algorithm can be used tocompute functional proximity.

Any of the coordinate, connectivity, graded, vicinity, navigation,trajectory, path, graph or other measures described herein may be usedin conjunction or alone to determine functional proximity. Functionalproximity algorithms can use these measures to find correspondence amonga set of reference points and define a correspondence based on themagnitude and category of relationships among a plurality of the dataentities.

Functional Vicinity Algorithms

A functional vicinity can be defined which provides, for any set offunctional coordinates, a region or subset of the space based on a firstselected reference point and the surrounding area. In some embodiments,functional vicinity can be defined as the subset of entities inn-dimensional space which are located within a threshold functionalproximity of a first selected and defined reference point. In such anembodiment, the functional proximity threshold defines a distance withinfunctional proximity space that allows for the inclusion of referencepoints within the threshold distance and the exclusion of referencepoints outside of the threshold distance from the first definedreference point.

Functional Navigation Algorithm

In some embodiments, through the establishment of a functionalcoordinate system and corresponding functional proximities betweenreference points within that system, a connected network of entities isestablished. A path travelling along these connections may beconstructed as a path to navigate between reference points within thesystem. In some embodiments, a functional path defines a set magnitude,distance, or route among a series of reference points within then-dimensional space.

When navigating between a first and second reference point, a multitudeof paths can be proposed to reach the second point by selectingdifferent reference points of varying functional proximity. As anon-limiting example, a path can be selected among this set of paths byoptimizing among all possible paths by minimizing the functionalproximity of the entire path. Thus, the optimization process affectsnavigation as well as the orientation towards the second referencepoint, and consequently identifies an efficient or optimized path.

In some embodiments, path optimization may be used to improve astatistical outcome in a biological system, by choosing a path that isbiologically efficient.

Functional Trajectory Algorithm

Using paths between reference points, a trajectory can be establishedover time by representing a set of paths through functional locations inthe n-dimensional space to infer an outcome in the underlying functionalsystem, as verifiable through a test of statistical significance. Thus,trajectories can enable the derivation a velocity in functional space byobserving movement through time, and can further enable the inference ofa future location by observing that trajectory relative to past andpresent position.

A path travelling along these connections may be constructed as a pathto navigate between reference points within the system. In someembodiments, a functional path defines a set magnitude, distance, orroute among a series of reference points within the n-dimensional space.

Accuracy Scoring Systems

A scoring system can be defined which provides, for any pair of tags, ascore based on a type of proximity to convey the accuracy of assignment.As a non-limiting example, such a type of proximity could include thelikelihood that two independent parties considering a particular entitywould select either tag to characterize the entity. In such a case, ifboth tags describe an entity with reasonable accuracy, then their scorescan be high. In a case where the tags diverge substantially from eachother, then the scores can be low. Types of proximity for the purposesof creating scoring systems can, in some embodiments, be based on otherfunctional proximity algorithms. In other embodiments, they canprimarily encode human intuition about semantic similarity within thelanguage described herein.

For scoring systems which provide scores based upon human intuitions ofsemantic similarity, the resulting metrics can be combined with otherproximity metrics to create new composite metrics. Applications include,as non-limiting examples, classifier assessment and functionalinformation system maintenance.

Dynamic Syntactic Affinity Group Formation in a High-dimensionalFunctional Information System

In certain embodiments, a systems syntax is constructed, enabling theevaluation of combinations of elements of an underlying system. Theseelements are organized functionally, wherein a function comprises thetransformation of inputs to outputs. The systems syntax is representeddigitally. The system has parts, processes, relationships andattributes, which may, in certain embodiments, be representedrespectively by nouns, verbs, prepositions and conjunctions, andadjectives.

The elements of this system can be encoded based on their roles ininput-output processes. In graph representations of the system, theparts and processes can be represented by nodes and the relationshipscan be represented by edges. In other embodiments, code sequences mayrepresent nodes and the interactions among the code sequences may berepresented by edges. The syntactic and graph-based methods ofrepresenting the system can be complemented with semanticrepresentations, including natural language tags corresponding to theelements of the system; they can also be supplemented by visual, aural,or audio visual representations. They can be connected to metrics whichmay represent properties, results, or aspects of the system. These canbe integrated with other classification systems for organizing data,including coordinate, network, and hierarchical methods, including, butnot limited to, temporal and geographic representations. In certainembodiments, the data structure may facilitate analysis across context,time, and geography unified by functional analysis, and may enhance thecapacity for flexibility of search, recommendation, and analytics acrosscontext.

Encoding the elements of the system according to their input-outputproperties enables them to be mapped into coordinate space, whichfacilitates computation of distance and similarity. When represented asa graph, one can use graph algorithms to assess proximity and similarityamong elements. These can be combined with semantic measures ofdistance, including, as non-limiting examples, through algorithms suchas Word2vec and Doc2vec. Semantic similarity assessments can be enhancedthrough the use of graph representations of terms including, but notlimited to, using a wordnet. These can be further integrated withhierarchical representations of data that have been used to organizeinformation in particular domains. Weightings or scores can be appliedthat indicate shorter distances amongst elements that have beencategorized together through multiple layers of a hierarchicalstructure; these may include but are not limited to, techniques fororganizing information such as the Dewey decimal system, the Linnaeantaxonomy, and systems for organizing economic and financial datahierarchically such as GICS and NAICS. In certain embodiments, aweighting method may be defined as

${d\left( {x,y} \right)} = \frac{D - {R_{c}\left( {x,y} \right)}}{D}$

Where D is the weight of the maximal path through the taxonomy, w_(r) isthe weight assigned to an exposure r and R_(c)(x,y)is the set ofexposures that entities x and y have in common. In other embodiments,different algorithms will be used to assess similarity in a hierarchicalstructure. In other embodiments, similarity will be computed acrossnon-hierarchical data. These methods can be further fused withsystems-based methods of organizing data including in fields such asinternet network analysis, systems biology, and systems chemistry,including, but not limited to, networks of chemical reactions and foodwebs.

Maps of digital social interactions can be characterized in graphstructures through nodes and edges permitting graph algorithms to be runfacilitating those computations. The basis for integrating theserepresentations together lies in the capacity of the representation ofthe underlying functional system across domains, so that, for instancerepresentations of chemical pathway data in chemistry-specificclassification systems can be connected in graph space to the codeassigned to them in the system linking domains. In certain embodiments,the capacity to render the underlying system abstractly using thesefunctional models enhances the ability for a functional informationsystem to enable interventions or modifications, or to provide search oranalytical results related to the underlying system.

Weighting functions may be assigned which may, as non-limiting examples,assign greater weight to instances that are more recent; as anon-limiting example, a decaying function model may be used reflect theincreasing reliability or relevance of newer information. In certaincases, techniques such as function rank, assessing the most reliableparts of an input-output network by inward and outward edges andrecursively assessing their strength, can be fused to modify weightingschemes. Digital representations of these systems can be set and thenmodified based on ongoing user feedback on a digital platform, which canbe configured to provide, as non-limiting examples, search,recommendation, navigation, analytical, data feed, transaction, network,and security modules.

Inputs to the platform may be provided, as non-limiting examples, insemantic, syntactic, visual, aural, and tactile forms. The platform candetect or request preferences from a user; in certain cases these may beexpress preferences, as a user may be required to indicate certainaffiliated organizations or rank the importance of variouscharacteristics to the users' objectives; or they may be partially orfully implied, derived based on the user's interactions with theplatform.

The system may provide filters to the user which may be rigid, andcontrolled, as a non-limiting example, through boolean operators,matching which is based on relative rather than absolute preferences, orfuzzy (inexact) matching. Algorithms as applied to the network andcoordinate space may be assigned to the representation of the underlyingfunctional system to assess likely affinity amongst the elements of thesystem; the elements may be economic or non-economic and can rangeacross scale, time, and geography. The suggestions of likely affinityamongst the users may be contextualized depending on, as non-limitingexamples, whether the purpose is facilitating biological interaction,chemical interaction, economic or financial interaction, communication,or political interaction.

On an ongoing basis, the platform will gather information pertinent tothe evolution of an underlying functional system and use it to modifyits suggestions of affinity. As a non-limiting example, the informationsystem may apply functional tags to a set of generalized and specificentities and relate them across graphs and subgraphs. In developingaffinity metrics, the system will include algorithms for ascertainingthe diversity of affinity groups and corresponding robustness orresilience to events. It may, in certain embodiments, include asimulator tool to assess potential modifications to the system and thelikely response of the group, and will deploy techniques, including, butnot limited to, agent-based modeling and systems dynamics modeling todetermine probabilistically various time-series paths that may occurwithin a group or in the larger system. It may rely in part on therelationships amongst the groups and reflected within the model of thesystem to assess potential future trajectories and paths. The systemwill run statistical tests to try to determine correspondence betweenfunctional patterns and quantitative metrics, determine whether they arefunctional outcomes, and use this to improve recommendations forgroupings as well as potential trajectories and the provision of searchand recommendation outputs to users of the digital system. Underlyingalgorithms may provide arbitrary weightings to the various dimensions orsubcomputations of similarity, which may be personalized to one or moreusers or contextualized based on the group and its history ofinteracting with that platform as well as other empirical dataconcerning that group. The system will be designed to facilitatesimulation of complex systems in a more efficient, cost-effective, saferand more reliable manner then running the experiment empirically.

Derivatives of Functional Location

The assignment of entities in functional space to coordinate locationsthat can be rendered in an arbitrary number of dimensions can enable theidentification of functional entities with a set of points. In certainembodiments, functional location is a set of attribute and value pairs(a, v) that can be associated with an entity that describes an entity'srole in a system. Sets of functional entities that are interacting may,as a non-limiting example, exert influences on one another. Mathematicalderivatives may be performed, as a non-limiting example, on a locationor set of locations in functional space. As a non-limiting example, analgorithm may compute the functional velocity of an entity representingelements to ascertain the rate of change. As non-limiting examples, thederivative may be taken against time, geography or any quantity that canbe rendered in coordinate space. As a non-limiting example, thederivative may be a partial derivative. Successive derivatives may betaken, enabling the algorithm to compute the functional acceleration orrate of change of velocity; the functional jerk as the 3rd derivative;and successively higher-order derivatives. In some embodiments, thefunctional system may be configured to take the location in functionalspace or a set of its derivatives as inputs to an algorithm that, as anon-limiting example, may determine what entities will be recommended toa set of users.

Functional Proximity and Vicinity

Measures of distance may be computed, in certain embodiments, using afunctional proximity algorithm that takes as an input two or moreentries comprising locations in functional space, as a non-limitingexample, and returns a quantitative or qualitative assessment of theextent of similarity or path between those points. As a non-limitingexample, computations of functional proximity also may occur in graphrenderings of the location in functional space. An arbitrary distancemay be defined in high-dimensional or network space around a set ofpoints, and entities falling within that distance can, as a non-limitingexample, be categorized within a functional vicinity. A functionalvicinity algorithm takes as an input a set of locations and a quantifieddistance, as a non-limiting example, and returns a functional region.

Functional Regions and Trajectories

A functional region, in certain embodiments, comprises a set ofproximate points in functional hyperspace. As a non-limiting example,the identification of a functional region may enable a user of a digitalplatform to more effectively navigate search and locate other users. Afunctional trajectory algorithm, as a non-limiting example, maydemarcate or determine a set of paths that can be followed amongst theplurality of locations in functional space. A functional trajectoryalgorithm, as non-limiting examples, may include computations ofgeographic, functional, temporal, or other quantifiable data as a meansto ascertain a set of paths. In certain embodiments, an optimizationalgorithm may be combined with the functional trajectory algorithm,enabling a digitized representation of a functional system to providesuggestions or search results to a user regarding potential paths to betaken within a region in functional space.

Functional Centroids

In certain embodiments, complex computations amongst the set of elementsmay be enabled through the application of a heuristic and itsassociation with an algorithm as applied to a point in that region,which may, as a non-limiting example be termed a centroid. A functionalcentroid, may, as a non-limiting example, represent the weighted averageof the coordinate locations in functional space in which the weightingmetric may be associated with biological data, economic data, financialdata, or genomic data. To facilitate the computation of a centroid,algorithms may be designed so as to enable the computer to moreefficiently, rapidly, and precisely route and direct users amongst theelements of a functional system by demonstrating their representation infunctional space.

Functional Mass

A functional mass may be defined by assigning weights to differentlocations in functional space. These weights may be derived, asnon-limiting examples, from economic, geographic, temporal, semantic,syntactic, biological, or financial data. The assignment of weights andthe resultant mass may enable, in certain embodiments, the provision ofinputs to a center of mass algorithm that determines the centroid basedon the weighting function associated with the mass. As a non-limitingexample, the mass may then be used as an input to computer functionalforce exerted by a set of functional entities.

Coefficient of Function

In certain embodiments, a spectrum may be delineated Indicating theextent to which as non-limiting examples, the location, time, set offunctional locations, quantity, entity, data entity, semantic entity, orsyntactic entity, are associated with function, The spectrum may, incertain embodiments, be defined qualitatively or quantitatively. Incertain embodiments, a set of points, data entities, or functionallocations which are integrated, as non-limiting examples, with genomic,biological, syntactic, semantic, visual, aural, temporal, orquantitative data may serve as inputs to a functional proximityalgorithm or functional influence algorithm to determine the level ofassociation between that data and entities which are defined throughinput-output processes. In certain environments, the coefficient offunction may be normalized as a quantity between zero and one,inclusive. In other embodiments, the coefficient of function may benegative or may not be normalized. In coordinate representations of afunctional system, as integrated with other data, proximity algorithmson vector or tensor representations, as non-limiting-examples, mayenable the determination of a coefficient of function. In certainembodiments the coefficient of function may be expressed qualitatively;in others, it may be expressed quantitatively. In other embodiments, athreshold value may be set so that entities above a certain coefficientof function are deemed functional and entities below a certaincoefficient of function are deemed non-functional. In otherenvironments, entities with a negative coefficient of function or whichcounteract or are negatively associated with function may be deemedanti-functional,

Functional Force

In some embodiments, the coefficient of function may be an input to thecomputation of functional force; in other embodiments, the functionalforce may enable the computation of the coefficient of function. Afunctional quantity may influence, as non-limiting examples, functionaltrajectory, velocity, or acceleration of entities in the region. Innetwork representations of the functional information system, graphalgorithms may be computed, including but not limited to, betweennesscentrality and path algorithms.

Functional Markers

In certain embodiments, a set of functional markers may be defined whichenable the delineation of proportions, tendencies, and the distributionof functional entities within the functional system. In certainembodiments, a functional marker is a semantic, visual, auditory oraudiovisual tag applied to a set of functional data. In otherembodiments, a functional marker may represent a nexus associatingfunctional data, relationships, and a signifier. The set of functionaldata may be expressed, as non-limiting examples, as a set of codes, afunctional sequence, a subgraph of a functional graph, or otherrepresentations of functional data. In certain embodiments theidentification of functional markers enables the provision of a searchinterface to a set of users who need not be familiar with the functionalcodes or computations within the functional system to be able to accesssearch, recommendation, and navigation results.

Functional Communities

In certain embodiments, a community may be defined, as non-limitingexamples, through functional, qualitative, quantitative, geographic,temporal, semantic, syntactic, biological, and genomic data. In certainembodiments, functional community may coincide with a functional region,which is computed, as non-limiting examples, through the algorithms andmethods described herein. In other embodiments, functional communitiesmay be defined through affinity groups. In other embodiments, the unionof a set of functional locations. In certain embodiments, functionalcommunities or affinity groups may be identified, as non-limitingexamples, through a community detection algorithm or a clusteringalgorithm, including, as non-limiting examples, through spectralclustering or k-means clustering. With respect to entities, in certainembodiments, the functional union of a set of entities the sharedfunctional location of a set of entities (E) is the intersection of thefunctional locations of each entity e∈E. If E is a singleton set, i.e.,E={e}, the shared functional location of E is the functional location ofe.

The extent to which a functional community exhibits similar anddivergent proportions of functional markers may enable the algorithmicdetermination of the extent to which a community is similar to ordiverges from a reference community. In certain embodiments this mayfacilitate the statistical analysis of interventions within a community,as non-limiting examples, through studies, meta-studies and scientifictrials.

Functional Generative Networks

In certain embodiments, the capacity to model functional systems usingthe data structures described herein, integrate them with other methodsof organizing data, and simulating their performance can be integratedwith techniques for generating and determining outcomes within networks.As a non-limiting example, generative adversarial networks make may becombined with the methods described herein to develop optimal models orimproved models for synthesis, performance, or intervention within thereferent functional system.

Semantic Proximity of Functional Attributes

By applying functional keywords to entities in an information system,including, as a non-limiting example, a functional information system,the functional entities may be clustered by the semantic proximity ofthese keywords. As a non-limiting example, the clustering may occurusing a word embedding algorithm, including, but not limited to, theDoc2Vec algorithm, the Word2Vec algorithm, and the GloVe algorithm. Thisapproach, as a non-limiting example, enables the unification of a set oftext within the functional space, enabling, in certain embodiments,queries of functional space using natural language phrases.

Entities categorized according to functional codes may, in certainembodiments, may be transformed through a word embedding algorithm inhyperdimensional space so that semantic meanings are rendered as tensorsor vectors.

In certain embodiments, k₁, k₂, . . . k_(n) can represent a set of nkeywords for functional entity k. The centroid is defined, in certainembodiments as

$C_{centroid} = {\frac{1}{n}{\sum\limits_{i = 1}^{n}\;{{glove}\left( k_{i} \right)}}}$

The centroid can be thought of as the average meaning of all keywordsassociated with a company.

In certain embodiments, dimensional reduction or projection may enablediagnosis, search, visualization, or recommendation of outcomes in thefunctional system. As a non-limiting example, the semantic proximityalgorithms described herein may be unified with other proximityalgorithms, including, as non-limiting examples, functional proximityalgorithms, geographic proximity algorithms, temporal proximityalgorithms, syntactic proximity algorithms, Euclidean distancealgorithms, and Manhattan distance algorithms to enhance the precisionand accuracy of search, recommendation, matching, and analytical resultsin the functional information system.

Application: Labor

In certain embodiments, the application of the techniques and algorithmsdescribed herein may enhance a database associated with workforce,labor, or job data. As non-limiting examples, the information systemsmay be used for workforce predictions, workforce optimization, labor andeconomic policymaking, recruitment, job matching, skill assessment, jobtraining, candidate and job recommendations, experience matching, jobidentification, transferable skill identification, labor search results,labor simulation, labor modeling, labor analysis, industry trajectories,job trajectories, job search results, job matching, candidaterecommendations, advertising, marketing, sales, human resources,outsourcing, contracting, partnerships, entrepreneurship, investment,acceleration, incubation, economic matching, and transactionfacilitation.

Application: Policy

In certain embodiments, the techniques and algorithms described hereinmay be used to develop or enhance policy related to functional data. Asnon-limiting examples, the information systems may be used for laborpolicy, industrial policy, economic policy, city planning, monetarypolicy, fiscal policy, tax policy, trade policy, economic analytics,economic modeling, economic simulation, economic forecasting, tradeprojection, economic diplomacy, wage projection, zoning, real estatepolicy, central banking, infrastructure, currency stabilization,exchange policy, privatization, and planning.

Application: Finance

In certain embodiments, the techniques, methods, algorithms, andtechnologies described herein may be used in association with financialmarkets. As non-limiting examples, the information systems may be usedfor investment management, banking, risk management, financial analysis,audit, financial fraud detection, mobile banking, lending, borrowing,insurance, financial simulation, financial modeling, financial dataanalytics, currency trading, arbitrage, payment systems, investmentbanking, capital markets, trading, securitization.

Application: Clinical Trials

In certain environments, biological data organized according to functionmay facilitate the organization of heterogeneous data that cuts acrossscale, time, geography, context, code base, and natural languageterminology to enable the determination of large-scale trends andtendencies in biological populations. In bioinformatics and publichealth, assessing the prospective, historical, and current outcomes ofclinical trials can facilitate more precise, targeted, and effectiveinterventions by clinicians within a functional system. In certainenvironments the functional system, as embodied in abioinformatics-oriented functional information system, may be simulatedthrough techniques described herein as a means to assess perspectiveinterventions and algorithmic context before electing to do so withinthe functional system itself. Such a methodology may in certainenvironments, increase the speed, precision, accuracy, and safety ofinterventions within the functional system.

Application: Synthetic Biology

In certain environments, the combinations of elements delineated in thesystem syntax as applied to a bioinformatics database organizedaccording to the functional information system principles herein mayprovide a mechanism to generate and synthesize biological entities,including, but not limited to, within the laboratory context. Abioinformatics database containing information about the associations,outputs, outcomes, and effects of empirical, clinical, and theoreticalbiological populations, entities, and systems may enable the algorithmicdetermination or combinations of parts. In certain embodiments it mayimprove the safety, efficiency, and precision of biologicalinterventions in the functional system.

Application: Genomics and Bioinformatics

In certain embodiments, the methods described herein may be used toenhance biological databases, including, but not limited to, genomic andbioinformatic analysis. As non-limiting examples, the genomic andbioinformatic analysis may be used for gene editing, drug discovery,toxicology, crop modification, drug development, protein synthesis, andgene alignment.

Application: Evolutionary Modeling

The computation of these metrics may permit, as a non-limiting example,enable computational evolutionary models of a functional system. A setof functional entities may be selected at time t=0. The system syntaxprovided as an input to the functional information system governs theprinciples for the combination, disassociation, evolution, andextinction of the entities within functional space. As a non- limitingexample, the systems syntax may permit the combination of entities at agiven distance metric from one another within functional space, or thatshare certain attributes, characteristics, and properties in common. Inother instantiations of the functional information system, input outputmodels of the elements of the functional system may govern theprinciples for association and disassociation. As non-limiting examplesof the entities within the functional system, geographic, quantitative,or qualitative attributes may be associated with the entities.Parameters provided to the system, as non-limiting examples, may belayered with systems dynamics models, agent-based models, or functionalmodels that govern the growth and decay of parts of the system. As anon-limiting example, a logistic growth function may describe the changeover time of the proportion of entities in a functional subsystem,within a functional subsystem, as well as in the super system thatcontains it.

Regions of functional space may be defined across multiple domains,permitting the composition of domain-specific classification systems, asa non-limiting example, to enable the construction of pathways in thefunctional information system across these divergent classificationsystems which the computational models and algorithms characterizedherein, as non-limiting examples can permit the identification,assessment, quantification, and simulation, as well as retrodiction andprediction of outcomes, outputs, and results in the functional system.In certain embodiments the simulation models may provide results over aprobability distribution. In certain environments the system and itsforecasts may be deterministic. In other embodiments the forecast may benondeterministic. The complexity of this system and its functionalelements, reflected by, as non-limiting examples, heterogeneity, scale,and scope, may determine the utility of models for forecasting outcomesin the functional system.

Applications: Functional Search and Navigation

In some embodiments, the techniques described herein can be used toimprove the search and navigation of information relating to functionalsystems more rapidly, efficiently, and precisely than priormethodologies by utilizing functional relationships and functionalproximity metrics to relate and display multilayered query results. Insome embodiments the techniques may generate novel results, drawing uponfunctional groupings difficult to capture without functionalcharacterizations.

Key components of search and navigation in functional informationsystems are functional search algorithms that enable search andnavigation functionalities in and around locations or regions of thesearch space based on functional positions and functional proximity,each informed by the functional information, functional measures, orcharacteristics associated with the elements of the underlyingfunctional system. Functional positioning algorithms, as describedherein, provide information to locate untagged entities in functionalspace. In functional proximity algorithms, as described herein, eachmeasure or characteristic associated with a specific functional locationcan further inform the computer about an entity, providing a richcontextualization based upon its functional location. Functionalproximity and functional positioning algorithms are important componentsof search and navigation in functional information systems.

Assisted functional search, in some contexts, can allow users to searchand navigate nested functional coordinate-based systems. Users can inputa search or navigation entry, including, as non-limiting examples,natural language, sound, coordinate, and visual terms, and receiveexpected results corresponding to the specific domain and scale of thequery performed. In some embodiments, the returned results can includeinformation from other domains and scales, which is related to theoriginal search or navigation entry or search results by functionalassociations. These functional associations can be absolute, relating toat least one reference point in n-dimensional space, and they can berelative, contextualized to a user's specific functional identity andsummation of user-specific functional and non-functional attributes.

Users can navigate through multilayered search or navigation results andrepresentations of functional information by reorienting on a fixedpoint in order to iterate through successively related units offunctional information. Reorientation can occur around the function,level of granularity, or functional system. As non-limiting examples,users can receive information about function A at level X of granularityin functional system R, utilize a functional association to receiveinformation about function B at level X of granularity in functionalsystem R, utilize a functional association to receive information aboutfunction B at level Yof granularity in functional system R, and utilizea functional association to receive information about function Bat levelYof granularity in functional system S.

In a functional information system, iteration through successive searchterms is facilitated by functional relationships and functionalproximity. Using a functional information system, search resultsincorporate a quantitative proximity metric that facilitates userdiscovery of results, including as non-limiting examples specificoutputs being searched for and related outputs that were not initiallypart of the search but presented themselves as relevant throughfunctional associations.

In some embodiments, a user's ability to reorient queries and results onfixed reference points of functional information relies on a logicaldata model that specifies absolute and relative positions, quantifiablerelationships, and proximity metrics between data entities. In someembodiments, reorientation on functional information facilitatescomparative analysis between functional entities regardless of theirdomain, scale, and level of complexity.

Implementation of Search System: Construction of Reference Database

A reference database will be constructed using one or more of thelogical data model, stratified lexical architecture, and functionalsystem, coordinate or graph representation methods described herein. Insome embodiments, the reference database will comprise a feature setthat can enhance a machine learning technique.

The database will include a set of data D extracted from one or more oftext, document, video, audio, or image data. A plurality of entries in Dcan be associated in the database with a set of entries of functionalcodes, C, that can be rendered, as a non-limiting example, using thestratified lexical architecture or systems syntax described herein. Insome embodiments, the codes C will be assigned algorithmically; asnon-limiting examples, the assignment can occur through an expertsystems approach or a neural network model.

In some embodiments, a plurality of entries in C and D will beassociated with a set of probabilities Π that demarcate the likelihoodthat a subset of C corresponds to a subset of D; as a non-limitingexample, these probabilities will be derived through a machine learningtechnique.

In some embodiments, the database can contain a set of functionsF=f_(1,2 . . . n), wherein a subset of F corresponds to a subset of Cand D, that indicates, as non-limiting examples, common properties,attributes, values, relationships, bodies, or entities in the functionalsystem. As non-limiting examples, the correspondence among subsets of F,C, and D can be derived from analysis of the systems syntax and of agraph in the functional information system.

In some embodiments, the reference database can qualitatively orquantitatively order the functions in the underlying functional systembased on, as non-limiting examples, the extent of the functions andrelationships among elements of the functional system. As a non-limitingexample, an equation from which the order is derived can be recursive,such that relationships or functions more than one degree removed from agiven entity or body e can impact the order of e or f with respect toother entities, bodies, relationships, or functions in the database. Asubset of the set of quantitative correlations or qualitativecorrespondences, O, that determine order, can be associated in thereference database with subsets of C, D, Π, and F.

Implementation of Search System: Search Processing

A search entry, which can, as non-limiting examples, include text,audio, functional coordinates, image, or video data, can be provided bya user. In some embodiments, the user, or the entities to which the useris related, can be a subset of the functional system.

In some embodiments, the engine will process the search entry to extractdata d_(m) related to, as non-limiting examples, functions, entities,elements, phenomena, attributes, relationships, or values in theunderlying system. If the engine has information concerning the user,the engine can, in some embodiments, extract data d_(u) concerning theuser and the entities to which the user is proximate in the functionalsystem. The engine, as non-limiting examples, can use either d_(m) andd_(u) or both in processing the query. The engine can compare d_(m) andd_(u) to the reference database.

In some embodiments, the functional information system will use amachine learning technique to probabilistically determine results giventhe search entry based on, as non-limiting examples, the referencedatabase, the media item, the user, D_(u), D_(m), C, D, O, Π, or F, orcombinations or subsets thereof. As non-limiting examples, thefunctional information system can probabilistically assign a set oflocations comprising a set of regions or subgraphs in n-dimensionalcoordinate space, graph space, or both, to d_(m), d_(u) , orcombinations or subsets thereof, with the search term and the user. Insome embodiments, the regions or subgraphs r_(m) and r_(u) correspondingto the media item and the user, respectively, will include subsets offunctional space probabilistically associated with the media item oruser, including connections, relationships, or areas of interest.

In some embodiments, the engine will use, as a non-limiting example, afunctional proximity algorithm to return search results to the user thatare proximate to r_(m), r_(u), or both.

In some embodiments, sets of locations l_(m) and l_(u) can be defined aspoints, nodes, or edges that are in, are functionally proximate to, orare in the functional vicinity of, r_(m), r_(u), or both. Sets ofweights w_(m) and w_(u) can be derived, as a non-limiting example, fromthe reference database and assigned to corresponding locations l_(m) andl_(u). In some embodiments, non-functional data can influence theweights and locations. In some embodiments, the locations l willcorrespond to the codes c, cεC, and the weights will be proportional toπ×o, πεΠ, oεO.

A centroid can be defined, in some embodiments, as the central locationof an entity's functional region, f, thereby defining the location ofthe centroid. The strength of the effects from each of the above may notbe the same, and these differences can be reflected in the definition ofthe boundary of the user's functional region. The identification of thecentroid can facilitate the analysis of large-scale functional systemsby expediting the computation of functional trajectories, forces, andn-body simulations among functional entities.

In some embodiments, interactions between entities in functional spacecan be represented as biases which can be computed among the locations,regions, or centroids. In some embodiments, the magnitude of bias can beprobabilistically inversely proportional to the distance between thelocations, regions, or centroids.

In some embodiments, user clicks, connections, screen time, otherrelated accounts, data, and responses to results will be tracked,permitting, as non-limiting examples, the user to be more accuratelyrepresented, the trajectory of entities to be more easily mapped, andthe engine to provide more precise search results in the functionalinformation system.

Search Results

Search results can be returned to the user, as non-limiting examples, assubgraphs of the graph, subregions of n-dimensional coordinate space,media items, web pages, maps, values, tags, attributes, codes, softwareapplications, lists of entities, bodies, or functions in the functionalsystem, augmented reality visualizations, recommendations, or potentialconnections, or some combination thereof, which can be ordered, asnon-limiting examples, quantitatively, qualitatively, probabilistically,syntactically, spatially, aurally, temporally, graphically, or somecombination thereof.

In certain embodiments, the techniques described herein can provide datato a user about related, proximate, or connected entities within thesystem; analytics regarding a subregion of functional space; subgraphs,subregions, or subspaces that are functionally proximate to the userand/or the search term; and recommendations regarding prospectiveactions within the system, as described further below.

Graphical Representations of Search Results

The methods described herein can be used to display the outputs offunctional searches using a graphical user interface. In someembodiments, functional media system applications incorporate agraphical user interface allowing users and computers to interact with acentralized data store.

In some embodiments, functional information about a set of data entitiescan be aggregated on a separate layer in a data store, such that userscan query for regions or sub-regions of the set of data entities withoutrequiring the system to recompute the distribution of functionalinformation from the original data entities for each query, enablinghigher calculation speeds across scales of query.

In some embodiments, the graphical user interface will render queryresults by graphically displaying the values of the outputs andrelationally ordering the values on the interface to representfunctional associations and proximity relationships among individualvalues. In some embodiments, the display will visualize successivelylarger nested categories of functional tags corresponding to each value.

In some embodiments, functional feature sets augment graphicalrepresentations of search results, creating an additional layer offunctional information as a result of the original search on functionalinformation. As a non-limiting example, regions can be defined on asub-set of the set of outputs received as the output of a search, suchthat the region indicates another layer of functional associations andproximity relationships resting on top of the functional associationsand proximity relationships present in the original data before thesearch was performed.

As a non-limiting example, the coordinate representation of a set ofdata entities can be displayed to a user as a basemap for arepresentation of a graph. In some embodiments, the basemap canrepresent the maximal set of possible nodes and connections in a graph;in other embodiments, the basemap can be a coordinate-based orientationfor a graph visualization.

The visualization of the combination of the graph and coordinaterepresentations can enable the visualization and analysis of patternsand connectivity in large aggregate data sets associated with systemsand subsystems. In other embodiments, the coordinate and graphrepresentations can be distinct. In some embodiments, an interface willbe presented to a user with a basemap in conjunction with, asnon-limiting examples, geographic, temporal, mathematical, visual,functional, semantic, or syntactic representations, or some combinationthereof. A user can select a region of functional, geographic, temporal,syntactic, coordinate, or mathematical space to query, visualize, sort,or analyze.

The ordered parts of a functional system can be visualized on agraphical user interface, enabling users to search and navigatefunctional information about the components and connections of afunctional system and sub-sets of the functional system. As non-limitingexamples, a user or computer can specify a set of parameters associatedwith the coordinate or graph representation of the functional system,which can include color, weight, size, thickness, time, location, ortype of proximity metric, and receive functional informationcorresponding to the parameters as a result.

Functional and Syntactic Machine Learning

The methods described herein can be used, as a non-limiting example, asa means to achieve a mechanism or tool that assigns functional orsyntactic locations to previously unidentified media and entities. Thedata systems described herein enable the synthesis of instruments thatachieve the classification at scale sought by those who deal withextremely large data sets, including uses in machine learning, documentidentification, image processing, and natural language parsing,potentially diminishing the quantity of data required for machinelearning applications.

In some embodiments, functional machine learning is an algorithmictechnique, that, as non-limiting examples, can be configured to assignfunctional tags to words in a document or images in a picture, and thenfurther probabilistically assign functional locations to the entitiescharacterized within that document or picture by using the word orimage-level tags.

In some embodiments, syntactic machine learning is an algorithmictechnique that, as non-limiting examples, can be configured to assignsyntactic tags to words in a document or images in a picture thatreflect their order in an underlying functional system, and then furtherprobabilistically assign locations in n-dimensional or graph space tothe entities characterized within that document or picture by using theword or image-level syntactic tags.

In some embodiments, functional feature sets for machine learningapplications can be defined as a collection of characteristics, builtfrom the structured representation of functional information in acomputing environment such as a functional information system Given anyentity in a functional system, functional feature sets can map to acollection of values which can be used in a machine learning model topredict specific outcomes or retrodict phenomena based on the entity'sabsolute and relative location in functional space, wherein functionalspace can be defined as a representation of absolute and relativelocations in an underlying functional system.

In some embodiments, syntactic feature sets for machine learningapplications can be defined as a collection of characteristics builtfrom the ordered representation of information in a computingenvironment that reflects the order of the underlying system beingmodeled. Given any entity in the underlying system, syntactic featuresets can map to an ordered collection of values which can be used in amachine learning model to predict specific outcomes or retrodictphenomena based on the entity's absolute and relative location in ann-dimensional or graph space representation in the underlying system.

Functional and syntactic feature sets can be relational insofar as theyspecify interrelationships or common properties between elements, andall elements represented by functional or syntactic information can beexpressed as a feature in a functional or syntactic feature set. Byreferencing elements and interrelationships of an underlying system,functional and syntactic feature sets can improve, as non-limitingexamples, the speed, accuracy, and precision of machine learningpredictions.

A set of outputs of a functional proximity algorithm can, in certainembodiments, comprise a training set for a machine learning technique.As a non-limiting example, the outputs can enable the more rapid orprecise prediction of a functional location in n-dimensional spaceassociated with a data entity in a test set. In other embodiments, theoutputs can enable the prediction of outcomes in the functional systemmore precisely, as determined by a test of statistical significance.

Notions of functional and syntactic proximity enable a machine learningsystem to have a more robust system for error correction. As anon-limiting example, a machine learning algorithm would take a set ofnatural language or image media describing a particular entity andassign a set of functional tags to each one. If entities described inthese documents were previously classified accurately from another setof documents, one could compare results between the two sets ofclassifications. Because there is a notion of proximity withinfunctional space, the predicted values can be systematically comparedwith one another to assess similarity. Instead of a binary indication ofthe correctness of classification, the level of incongruence can bequantified and measured by assessing the functional proximity among thepredictions. The resulting information can be fed back into the machinelearning algorithm, allowing for a more robust testing andclassification procedure, as discussed below.

The application of functional or syntactic machine learning thus allowsfor a predictive proximity layer to be applied to the machine learningprocess. If the algorithm makes predictions that are functionally orsyntactically proximate, each individual prediction and classificationcan have a higher degree of confidence associated with it. Conversely,if predictions are functionally or syntactically distant, eachindividual prediction and classification can have a lower degree ofconfidence associated with it.

In some embodiments, an application of functional or syntactic machinelearning can allow other previously more rigid applications of machineclassifications to be updated to include a functional attribute and afunctional or syntactic proximity dimension. If a machine learningapplication's required end classification groups can be differentiatedfunctionally or syntactically, then an updated machine learningapplication would require a set of functional coordinates to beassociated to the previously classified groups in order to increase theupdated application's confidence about its predictions.

In some embodiments, functional and syntactic machine learningtechniques allow for the ranking of search results based on features toassess how appropriate a member is within a group. As a non-limitingexample, ranking search results based on appropriateness can entailfirst selecting a set of documents and asking the question, “which ofthese entities is most likely an orthopedic implant?” and then narrowinga set of reports, websites, or filings from thousands to dozens or ahandful; this technique can also entail the ability to ask what entityof a set of data entities is the most “orthopedic implant”-like. Rankingis a machine learning output technique where the machine learningalgorithm sorts the inputted information according to which entitiesmatch a criterion the best. Therefore, the ability to grant rank or haveclasses of ranked entities becomes a feature usable to enhance searchresults for functionally or syntactically proximate entities, as thehighest-ranked classes probabilistically will be better classificationcategories and higher scoring as a result.

In some embodiments, functional and syntactic machine learningtechniques also enhance how functionalities such as autocamplete areemployed. Traditional, non-machine learning methods for autocompletingsearch queries involves gathering previously provided information, suchas past searches or indexed keywords and headers. The introduction offunctional or syntactic machine learning techniques can, in certainembodiments, add accuracy or a new dimensionality to autocompletion ofsearch results by suggesting functionally or syntactically proximateterms or results or natural language alternative words that are markedwith proximate functional or syntactic tags.

Further, different machine learning techniques can be applied tofunctional and syntactic sets of entities that were previously notpossible. As a non-limiting example, methods like k-nearest neighbors,clustering, or support vector machine can use a type of functional orsyntactic proximity to define distance in a representative space. Insome embodiments, the system can be implemented such that graphing a setof data entities enables representation of the probability.

In some embodiments, given past data and past classifications regardinga set of entities, a prediction of future functional coordinates can bemade on a given entity given similar past data. If an entity with afunctionally proximate associated past coordinate has a more recentlyupdated coordinate, then a prediction or functional projection can bemade on the original entity's coordinate. Non-functional data can alsobe incorporated into the prediction process, from common features anddifferences in past global events, geographic location, or other sharedattributes.

In some embodiments, a custom feature set can be constructed, which cancomprise, as non-limiting examples, a plurality of tags, metatags,strings, code sequences, nodes, edges, or outputs of functional orsyntactic proximity algorithms, which can be denoted, as non-limitingexamples, as vectors, tensors, matrices, or arrays.

In some embodiments, given some functional or non-functional data abouta particular entity, functional or syntactic machine learning techniquescan be applied to infer additional functional and syntactic informationabout the entity. As a non-limiting example, a machine learning systemcan use certain data to predict a location or area for the entity withinfunctional or syntactic space; the machine learning system can thenpredict particular information about the entity using the inputinformation in conjunction with information regarding other entitieswhich occupy a similar functional or syntactic space.

Learned correspondence among entities with similar functional, syntacticand non-functional data can be applied to predict the functionallocations and classification codes of additional entities in the system.

In some embodiments, feature sets for functional or syntactic machinelearning techniques are selected from among legacy codes, naturallanguage terms, documents, images, videos, metatags, syntactic tags,functional code sequences, functional locations, functional regions, andprobabilistic associations among combinations of the foregoing. A legacycode can be defined as non-functional, non-syntactic prior art data. Thefunctional or syntactic machine learning technique can select from amonglegacy codes, natural language terms, documents, images, videos,syntactic tags, functional locations, functional regions, and functionalsequences as outputs. As a non-limiting example, a functional orsyntactic machine learning technique will use inputs comprising legacycodes, associated natural language terms, and syntactic tags toprobabilistically predict a legacy code for an element of an underlyingfunctional system identified in a document in a test set.

In some embodiments, functional or syntactic machine learning can beapplied to topic modeling and document summarization. By applyingfunctional tags at the word level, the system is able to abstractlyrepresent tangible concepts in generalized, interoperable, manipulable,and information-dense terms.

Functional and Syntactic Recommendation Engine

The methods described herein can be used to make recommendations tousers of a functional information system. As non-limiting examples,these recommendations can be derived from the entities and theirsyntactic and empirical relationships; the functional, syntactic,temporal, or geographic tags, attributes, values, or metrics assigned tothe entities; the relationships or connections among the data entitiesin the syntax, graph, or database; the express and revealed preferencesof the users of the database or software; or the relationships of theusers in a network structured based on the techniques described herein.

In some embodiments, the functional algorithms described herein that areused for functional search can, as a non-limiting example, determine,correspond to, or influence the recommendations offered to users.

In some embodiments, entities sharing numerous recent or heavilyweighted relationships with one another, or with a common third party,will be proximate within one or more databases used to providerecommendations, while entities without common or current relationshipscan be distant within those databases.

User preferences, current user state, user data including historical andcurrent actions, and network positions, as described further below, canfacilitate the customization of recommendations based on functional orsyntactic proximity calculations. In some embodiments, users can inputtheir express preferences, whether syntactic, functional, non-syntactic,non-functional, or some combination thereof, and associated values intothe system upon registering to gain access to the database. In otherembodiments, these preferences or filters can be modified at any time,either through a separate module or by indicating a preference regardinga set of entities.

As non-limiting examples, one or more filters can be absolute, in thatthey permit the user to exclude or include certain relationships,attributes, tags, values, metatags, strings, or entities; one or morefilters can be relative, in that they enable the user to indicate theextent of a preference regarding certain relationships, tags, metatags,attributes, strings, values, or entities, where the system can alsosuggest non-requested results that are functionally or syntacticallyproximate to explicit search.

Users can also reveal their preferences through interactions with dataentities, or other users, associated with the system. In someembodiments, preferences will be revealed by tracking user accounts,monitoring screen time, clicks, and other actions performed on thesystem, and using machine learning approaches to improve dynamically thecustomized recommendations to a user based on preferences. In someembodiments, users can upload a set of entities, relationships,attributes, values, or preferences to the system, which can be used toguide customized recommendations.

Network position can facilitate proximity calculations and dynamic,customized recommendations. The computer system can track connectionsamong users and the extent of their interactions. In some embodiments,strong connections among users on the system will lead theirrecommendations to converge significantly, weak connections will leadthe recommendations to converge slightly, and numerous degrees ofseparation will lead the recommendations to diverge.

In some embodiments, similarities among users in the system can lead therecommendations provided to them to converge, while differences amongthe users can lead the recommendations to diverge. As a non-limitingexample, the system can refine customized recommendations at varyinglevels of specificity based on changes in the network of users, theirpreferences, or the tags, attributes, values, relationships, metatags,strings, or lexical units assigned to the entities.

The results of functional or syntactic proximity algorithms can, in someembodiments, be used as inputs to recommendations. As a non-limitingexample, a user can seek a recommendation regarding an entity at acertain degree of removal within the functional system. A functional orsyntactic proximity algorithm can be selected which accounts for degreesof removal through alignment-based modifications.

In certain embodiments, non-functional data can be used, in certainembodiments, as an input to the recommendation engine described herein.As a non-limiting example, functional and geographic data can becombined; a recommendation algorithm can compare the extent ofsimilarity of a plurality of sequences, tags, or metatags in a givengeographic region, and derive comparative functional or syntacticproximity results among the plurality of sequences, tags, or metatags. Acomposite functional or syntactic proximity result can be derived, as anon-limiting example, through matrix multiplication. In certainembodiments, the comparative functional or syntactic proximity resultscan be reweighted by a set of metrics associated with the functionalsystem, the functional information system, the geographic region, or acombination thereof. In certain embodiments, the metric will be selectedfrom among the proximity result itself and a location-quotient basedmetric.

The recommendation engine can, in certain embodiments, use the proximityalgorithm derived from the combination of functional and geographic datato determine proximate geographic regions to a reference region. As anon-limiting example, the recommendation engine can then use anotherfunctional proximity algorithm to query for, as non-limiting examples,code sequences, paths, pathways, tags, or metatags that can modifyoutcomes in the functional system in the reference region. In someembodiments, the extent of modification can be compared with empiricaldata and verified through a test of statistical significance.

The prospective recommendations, in certain embodiments, can be adjustedthrough the use of a set of metrics which incorporate the prevalence oreffect of sequences, tags, codes, metatags, paths, or pathways byregion; as a non-limiting example, the metric chosen can be a locationquotient. In certain embodiments, the metrics chosen from a locationquotient, a simulated outcome in the functional system, and empiricaloutcome in the functional system.

Functional Media Systems (FMS)

Functional media systems optimize search and navigation of functionalinformation by streamlining operations by which an arbitrary number ofusers using an arbitrary number of applications can receive, send,create, and update functional information using a centralized data storethat manages linkages across applications and allocates information tousers based on their functional identity, the summation of functionaland non-functional attributes corresponding to a data entity or user ofa functional information system.

Constructing a Functional Media System

In some embodiments, a functional media system has an applicationslayer, including, as non-limiting examples, programs that allow users tointeract with functional information by reading, writing, updating, andtagging functional and non-functional data entities with, asnon-limiting examples, the metatags, code sequences, and stratified andsegmented lexical architectures described herein. A functional mediasystem can contain at least one user-facing application.

In some embodiments, applications in a functional media system are builton top of a data store that takes in information and indexes it for useby applications. The functional information system can have a serviceslayer. One or more roles of these services can be to electronicallyapply at least one functional tag to incoming data usingcomputer-assisted classification algorithms, or the data can alreadyhave at least one functional tag assigned to it upon inclusion in thesystem. The services layer then can categorize data and send it to astorage layer based on the type of data being manipulated, including asnon-limiting examples coordinate-based data, identifying entity data,and data related to performance within the underlying system or thefunctional information system.

In some embodiments, services or applications can draw on and contributeto the centralized data store when specific functional andnon-functional information is needed or created by an application. Otherapplications can register to access the data store, which can enable theapplications to automatically receive the propagation that a data entityhas changed upstream and immediately begin transmitting the updated dataentity for use.

Because the data store standardizes the capture, organization, andtransmission of information according to function, in certainembodiments, the applications drawing on the data store can communicatein a common standardized language to describe the data, which caninclude the stratified lexical architecture and syntactic taggingtechniques described herein, enabling streamlined system widecommunication of new additions or updates to the data store.

In some embodiments, specific applications can require one or morespecific layer abstractions that modify data received from or sent tothe centralized data store and convert it into a form that is optimizedfor that specific application and its users.

In some embodiments, the centralized data store of a functional mediasystem will communicate with applications layer in a variety of ways,including as non-limiting examples push notifications and point-to-pullnotifications, that manage linkages and facilitate messaging acrossapplications. These communications can be automated based on thefunctional identity of the user, recipient, or sender of information, aswell as the underlying data being transmitted, or can be requestedmanually.

Functional Media System: Applications

The methods described herein can be used in connection with a functionalmedia system that operates as a layer of operations that executes on topof a layer of functional information system operations for the purposeof creating and distributing functionally tagged information, such asmedia items, between users in a network.

In some embodiments, the applications layer of a functional media systemcan enable a distributed communications system that transmitsinformation and filters messages among users of a set of applications,according to the functional identity of the users, their current stateof registration and authentication, and the information beingtransmitted. Functional identity refers to the collection of values,attributes, and tags associated with a data entity in a functionalinformation system according to the absolute or relative position of itscorresponding referent element in the underlying functional system.

Each user of a functional media system and media item transmittedthrough the system can occupy one or more functional identities based onthe set of functional tags assigned to them representing their specificrole in the underlying functional system. Machine learning approachescan be utilized to assign functional tags and identities to users of afunctional media system and elements of a functional system.

In some embodiments, users of a functional media system share andreceive data feeds associated with the functional identity of the userand of the information itself. As non-limiting examples, users canreceive and access alerts or notifications from feeds of functionallytagged information, static as well as regularly updating databases offunctionally tagged information, and visualizations and analytics thatrepresent, summarize, and identify patterns associated with functionalinformation. Functional proximity algorithms and functionalrecommendation engine technology can be used to calculate the relevancyof a particular media item to a user of a functional media system, basedon a set of inputs including as non-limiting examples the functionalidentity of the user, and the browsing and transactions history andpreferences of the user as well as other users with a similar ordifferent functional identity. Functional identity can increase thedimensionality of search space by adding user-specific andfunction-specific dimensions.

In some embodiments, users of a functional media system shareuser-generated information with other users based on existing functionalrelationships, including as non-limiting examples, a functionalrelationship between the two users, between the two users and otherusers, between the users and other elements of the functional system;the functional relationship can include interest in a connection as wellas a pre-existing connection between two users of a functional mediasystem or elements of a functional system.

In some embodiments, users of a functional media system shareuser-generated information based on an interest in a functionalrelationship or element of a functional system, the interest beingindicated through a user request or other interaction facilitated by thefunctional media system. Users can browse or contact existingconnections as well as posited connections based on functionalrelationships, as non-limiting examples belonging to the same functionalsystem, having a shared need for a specific input, output, or process,and fulfilling a similar function in different or related systems.

Functional information systems enable search and navigation capabilitiesin functional media systems by filtering out irrelevant information andfacilitating identification of interesting and sought after information.In a functional media system, the types of data that are sent to usersor that users seek out is scoped by the functional identity of the useras well as the media being transmitted.

Functional Media System: Functional Media Markers

In some embodiments, machine learning approaches can be used to populateand structure functional media systems by assigning functional orsyntactic tags to all or part of large data sets associated withunderlying systems. The assignment of media markers can incorporate theuse of the logical data model, syntactic tagging, stratified lexicalarchitecture, graph, and coordinate representation techniques describedherein in a functional media systems context.

As non-limiting examples, a feature, attribute, or function, orcombination thereof, can be identified from a directory or library andtagged as an element of a media item. As non-limiting examples, mediaitems can be in text, audio, video, code, digital, any other type ofmedia that can be converted into a digital format, or some combinationthereof. A directory or library of media markers can be stored whichindicates the prevalence or location of a set of feature, attribute, orfunctional tags, or relationships among them.

In some embodiments, associations can be defined between sets offeatures, attributes, functions, tags, and media markers based onlinguistic, syntactic, semantic, graphical, auditory, visual, textual,or functional elements in a media item. A tag can be assigned to themedia item based on the prevalence or location of a linguistic,syntactic, semantic, graphical, auditory, textual, visual, or functionalelement, or the relationship among a set of elements. In someembodiments, the media item can be processed to relate it to otherelements in the database. As a non-limiting example, one or moredatabases can be configured based on an automated training process. Asnon-limiting examples, the machine learning process can be supervised,semi-supervised, or unsupervised.

In some embodiments, a confidence score can be associated between afeature, attribute, or functional tag and an element. The confidencescore demarcates the probability of association among the feature,attribute, functional tag, or element within a test set based on datafrom a training set. The media item can be processed to extractadditional functional tags to hypothesize a sub-library based on themarkers, enabling the determination of a confidence level for thecontextual library selection.

In some embodiments, a computer-assisted classifier can provide a scorebased on a plurality of features, tags, attributes, or functions.

In some embodiments, an element can be compared to a media marker fromthe library or directory and associated if there is a match above acertain threshold. A computer-assisted classifier can enable theassignment of the media marker to the element. As a non-limitingexample, a processor can extract relevant terms from the media orlibrary in the directory. The classifier can be configured with markersextracted from the media and their functions, tags, codes, attributes,features, or some combination thereof.

As a non-limiting example, this methodology can be used torecharacterize or change prior codes. A score can be assigned based on aset of parameters and algorithms to determine whether therecharacterized codes account for a set of phenomena in the system moreeffectively than previous codes.

In some embodiments, a functional application database can be stored,including, as non-limiting examples, information regarding functions,tags, attributes, or features. The processor can associate a classifierto an extracted element to classify it to a plurality of attributes,tags, functions, or features associated with a functional application.

In some embodiments, a user can be presented with an unstructured mediaitem and a set of scores, and a set of actions to be performed using anextracted parameter. As a non-limiting example, a user can have theoption to modify an intended action. The action can enable the user toview the media item, the received information, and the score of eachaction to assist the user to decide whether to modify and affectperformance of an intended action.

Application: Matching Multidimensional Projections of Functional Space

Some embodiments can include a method for algorithmically using ann-dimensional representation derived from a systems syntax forprojecting location or relationships associated with data entities inn+k-dimensional space, the method comprising: electronicallyrepresenting a systems syntax, wherein the systems syntax comprises alogical data model that can be applied by a computer processor toevaluate or generate expressions of elements, wherein the elementsrepresent parts, processes, and interactions of an underlying system;electronically receiving an input from a computing device, wherein theinput is capable of being represented as a functional location inn-dimensional space, and wherein the data entities at a functionallocation characterize one or more of the elements, and storing the inputas a data entity; wherein at least one of the dimensions in then-dimensional space represents a functional domain, the functionaldomain comprising attributes of roles, order, or relationships among theelements; electronically assigning a set of functional locations in then-dimensional space to the data entity, the locations based onattributes of the data entity; algorithmically computing a syntacticproximity among a set of functional locations by executing an algorithmbased on the systems syntax on a set of the locations in n-dimensionalspace, wherein the syntactic proximity characterizes a quantitative orqualitative measure of similarity amongst attributes of the elements ofthe underlying system with respect to a projection of the functionallocation; algorithmically computing a projection of location orrelationships associated with one or more of the elements in theunderlying system as represented by the data entity in the n-dimensionalspace, based on the computed syntactic proximity.

In some further embodiments, the methods can include algorithmicallycomputing a functional trajectory of the data entity based on arelationship of the data entity to reference points in the n-dimensionalspace or movement of the data entity with respect to the referencepoints, the trajectory representing a direction associated with a set ofpaths through functional locations in the n-dimensional space;algorithmically computing a functional velocity of the data entity basedon a measurement of a change of the location or relationships relativeto positions or the reference points at two or more points in time;using the functional trajectory and functional velocity as analgorithmic input to improve projective precision or accuracy.

In some further embodiments, the methods can include electronicallyconstructing a graph representation of a set of the locations inn-dimensional space by assigning nodes to a set of the parts andprocesses and edges to a set of the interactions or relationshipsamongst the parts and processes; algorithmically computing a graphproximity by executing an algorithm that computes similarity amongst theelements based on strength, quantity, or degree of connection amongstthe nodes and the attributes of the nodes in the graph representation;and

algorithmically computing a composite proximity by executing analgorithm that integrates the computed syntactic proximity and output ofthe graph proximity algorithm; using the composite proximity to increasethe precision or accuracy of the projected location or relationships.

In some further embodiments, the methods can include associating one ormore elements and a functional location with a set of users;algorithmically computing the syntactic proximity amongst a plurality ofusers or elements; applying a syntactic vicinity algorithm to define agroup of users and elements based on the computed syntactic proximity;predicting a quantitative or qualitative outcome for the group; whereinthe group exhibits a higher correlation to the predicted outcome thanthe elements that are not in the group, as determined by a test ofstatistical significance.

In some further embodiments, the methods can include wherein the groupcomprises a statistical control group, and wherein the syntacticvicinity algorithm executes steps for identifying a subset of the dataentities including the selected data entity in n-dimensional space whichare located within a threshold syntactic proximity of one or moreelements represented by data entities, further comprising: applying thesyntactic vicinity algorithm to a second group of users and elements;computing the syntactic proximity between the statistical control groupand the second group; using the syntactic proximity and the predictivequantitative or qualitative outcome or an empirical outcome from thestatistical control group to project an outcome for the second group.

In some further embodiments, the methods can include, wherein thefunctional domain is biological, and a plurality of elements areselected from among genes, nucleotides, proteins, molecules, organelles,organs, organ systems, organisms, species, populations, and ecosystems,further comprising using the syntactic proximity as a basis forpredicting, recommending, or engineering biological composition,structure, location, relationships, or outcome.

In some further embodiments, the methods can include wherein thefunctional domain is economic, and a plurality of the elements areselected from among individuals, jobs, skills, products, companies,resources, and activities; further comprising using the syntacticproximity as a basis for predicting, recommending, or engineeringeconomic composition, structure, location, relationships, or outcome.

In some further embodiments, the methods can further comprise:integrating the graph representation with a second graph representationsuch that the first graph representation comprises a subgraph;associating one or more elements with a user;

associating a set of metrics related to syntactic proximity to route theuser to alternate paths; and relating the set of metrics to predictedoutcomes in the underlying system.

In some further embodiments, the methods can include wherein the grouprepresents a geographic region, biological system, or grouping offunctional assignments, wherein the functional trajectory represents adevelopmental path for the geographic region, biological system, orgrouping of functional assignments, and

wherein the functional velocity correlates to a growth rate, furthercomprising computing the predictive functional location as an input to arecommendation engine.

In some further embodiments, the methods can include wherein thefunctional domain is economic and the syntactic proximity defines afunctional distance comprising a mapping from at least two points in atleast one dimension in the n-dimensional space to a real number, furthercomprising: algorithmically comparing the functional trajectory of aplurality of economic elements based on a set of qualitative,quantitative, geographic, or temporal attributes of the economicelements; using the functional trajectory as an input to a search,recommendation, matching, or analytical result provided to a user.

In some further embodiments, the methods can include identifying afunctional region proximate to the data entity in n+k-dimensional space;modifying the functional region based on a preference, or frominteractions between the data entity and other elements of thefunctional system; wherein the functional trajectory or functionalvelocity of the data entity corresponds to a path in the underlyingsystem or in a digital representation of the underlying system; andproviding a set of projections of code sequences, paths, pathways, tags,or metatags for modifying outcomes in the functional system.

In some further embodiments, the methods can include wherein the searchor recommendation result relates to economic, financial, or policyobjectives, further comprising providing a set of potential or actualeconomic incentives, tax policies, labor policies, workforce policies,industrial policies, monetary policies, fiscal policies, acquisitions,mergers, divestitures, or investments to a user.

In some further embodiments, the methods can include wherein the searchor recommendation result relates to workforce development or labor,further comprising providing a set of career paths, job opportunities,labor distributions, educational distributions, recruitment pools, skilllevels, job responsibilities, economic metrics, staffingrecommendations, or advertisements to a user.

In some further embodiments, the methods can further comprise assigningk-dimensions in the n+k-dimensional space to temporal, geographic,demographic, biological, genetic, financial, policy or economic data;wherein the data comprises quantitative, qualitative, textual, visual,aural, audiovisual, tactile information; computing a predictivefunctional location in the n-dimensional space based on a set of thek-dimensions.

In some further embodiments, the methods can include using a wordembedding algorithm that renders textual data based on semanticproximity to construct a subset of the n+k dimensional space based on acorpus; and integrating the semantic proximity and the syntacticproximity to enhance the computation of predictive functional location.

In some further embodiments, the methods can include constructing oraugmenting a corpus based on syntactic proximity in n+k dimensionalspace; using the corpus to provide or augment the predictive functionallocation or a search or recommendation result.

In some further embodiments, the methods can include wherein thestatistical control group comprises a work or labor force distributionof a region, company, sector, or industry, further comprising:associating a set of metrics or outcomes with the statistical controlgroup; computing predictions of a set of paths or locations in theunderlying system related to the work or labor force distribution of asecond region, company, sector, or industry; wherein a user isassociated with the second region, company, sector, or industry;providing recommendations to the user regarding paths or locations.

In some further embodiments, the methods can include executing a fuzzyquery where elements can be identified or matched based on theintersection of two or more functional areas defined by the syntacticproximity of their functional location.

Some embodiments can include a functional connectivity system comprisinga computing environment configured to perform a database operationutilizing a computerized representation of a functional system, thesystem comprising: an electronic data store comprising a set of dataentities in a database system, the data entities representing elementsof the functional system, wherein the functional system comprises agroup of related elements ordered by their functional roles inconverting inputs to outputs, or as the inputs, or as the outputs; anelectronic representation of a systems syntax, wherein the systemssyntax comprises a logical data model that can be applied by a computerprocessor to evaluate or generate expressions of elements, wherein theelements represent parts, processes, and interactions of an underlyingsystem; receiving a set of functional locations from a database, whereina function represents a conversion from inputs to outputs or a role orproperty in the conversion from inputs to outputs in the underlyingsystem and a functional location comprises a position of an entity as aninput, output, intermediate, relationship, or process associated withinputs, intermediates or outputs; algorithmically computing theproximity among a plurality of the entities or attributes representingthe entities based on their functional locations; and identifying ormatching the entities or the attributes representing the entities basedon the proximity of their functional locations.

In some further embodiments, the system can include whereinnon-functional attributes can be used as an input in the process ofidentifying or matching of entities, and wherein the functionallocations can be identified semantically, syntactically, graphically,symbolically, visually, or aurally; and wherein non-functionalattributes comprise an economic metric, a financial metric, demographicdata, geographic data, temporal data, or experiential data.

In some further embodiments, the system can include wherein thefunctional system is an economic system, and wherein the data entitiescomprise enterprises, individuals, products, franchises, facilities,resources, government entities, industries, sectors, independentcontractors, or nonprofits, further comprising identifying or matchingentities for communication, transaction, advertising, investment,taxation, incentive programs, policy measures, or donation.

In some further embodiments, the system can include wherein thefunctional system is an economic system, and wherein the data entitiescomprise jobs, skills, tasks, workers, workforces, employers,educational institutions, training institutions, and researchinstitutes, further comprising identifying or matching entities forrecruiting, job search, hiring, labor policy, workforce development,skill development, training, apprenticeship, coaching, mentorship,management, leadership development, entrepreneurship, incubation, oracceleration.

In some further embodiments, the system can include wherein thefunctional system is a biological system, and wherein the data entitiescomprise genes, nucleotides, genetic sequences, molecules, expressedproteins, biological organisms, organelles, organs, organ systems,species, or populations, further comprising identifying or matchingentities for bioinformatic analysis, synthetic genomics, gene editing,or drug discovery.

Application: Data Filtering

The methods described herein can be used, in certain embodiments, tofilter data or information related to, as non-limiting examples,functional, geographic, temporal, physical, chemical, biological,visual, or aural systems, or representations thereof. As non-limitingexamples, the filtering can be lossless or lossy. In some embodiments,as non-limiting examples, the data filtering can be grammar-based,graph-based, semantic, syntactic, image-based, matrix-based, or somecombination thereof.

Application: Process Improvement

The models described herein can be used, as a non-limiting example, toimprove the allocation or flow of resources throughout an underlyingfunctional system, which can comprise at least one network, sub-network,or sub-system. The associated algorithm can be a response to a searchrequest from a user; in some embodiments, the capacity to demarcatefunctional attributes of the user and location of the user in thefunctional system will enhance the optimization process.

In some embodiments, properties related to the functional system, which,as non-limiting examples, can be temporal or operational, will be usedas inputs to an improvement process, in which different functionalcomponents will be reengineered or redesigned based on the precedinganalytical process.

In some embodiments, the capacity of the logical data model, syntactictags, and representations in functional n-dimensional and graph space tomap underlying functional systems and their interrelationshipsfacilitates targeting improved outcomes for sub-systems and processes inthe underlying functional system, while accounting for effects onrelated sub-systems and processes. Targeting improved outcomes caninclude improved outcomes for the underlying system as a whole as wellas for specific sub-systems and processes.

The model can be applied, in certain embodiments, to analyze functionalsystems to understand scenarios and decision processes and can use, asnon-limiting examples, functional and syntactic proximity, ranking, andscoring systems to evaluate outcomes. In some embodiments, a machinelearning process can be designed which takes as inputs large datasetsassociated with the correspondence among outcomes in the functionalsystem and locations in functional space; develops a probability spacebased on that correspondence; uses a feature set comprising thecorrespondence, the probability space, and the input data; chooses aplurality of variables to optimize; and assesses the probability ofoptimal outcomes for a test set.

Application: Organizing Links Among Platforms

The techniques described herein can be used, in certain embodiments, todevelop an underlying ontology or systems syntax among, as non-limitingexamples, databases, applications, software tools, and platformscharacterizing or modeling, as non-limiting examples, a complex systemor functional system. The linkages reflected through the ontology orsystems syntax can facilitate the interoperability of the databases,applications, software tools, platforms, or some combination thereof.

In certain embodiments, the techniques described herein can provide aunifying mechanism to regulate and manage functional systems, which canbe facilitated through the development of a visualization tool thatrelates, as non-limiting examples, the tools and platformscharacterizing the underlying systems.

Application: Systems Analysis

The methods described herein can permit the computation of expressionlevels of populations in complex or functional systems across, asnon-limiting examples, scale, time, geography, and domain to enhanceanalytics and queries within the functional information system as wellas to improve intervention within the complex or functional system. Thetechniques described herein related to descriptive analytics can improvethe capacity to understand the composition or properties of a pluralityof subsets of a functional system; in some embodiments, the techniquesdescribed herein may be applied to improve the messaging and connectionswithin a functional media system.

The capacity to map the trajectory of elements, as non-limitingexamples, can facilitate improved forecasting regarding the futureproperties, attributes, or locations within the functional system orrepresentations thereof. In some embodiments, the predictive analyticsdescribed herein can, within a functional media system, influenceactions taken by a plurality of users.

The capacity to tag large population sets can facilitate, asnon-limiting examples, reorganization, stratification, anddiversification according to functional or syntactic characteristics inconjunction with normative models. The use of normative analytics canenable more consistent achievement of statistical outcomes within thefunctional system or representations thereof, as determined by a test ofstatistical significance.

In some embodiments, a sub-element of an underlying functional systemcan be dependent on other elements of a functional system. In someembodiments, a super-element of an underlying functional system can bedependent on other elements of a functional system. As non-limitingexamples, the first sub-element or super-element can provide informationor energy to another element or to the larger functional system.

In some embodiments, syntactic and graph modeling techniques can enableusers to query, visualize, and analyze results relating to thefunctional system including as non-limiting examples for diagnosticpurposes and for predicting outcomes in functional systems.

Application: Systems Simulation

The methods of characterizing complex systems described herein can beused, as non-limiting examples, to simulate the performance or behaviorof a complex system under a set of parameters. In some embodiments,nodes can be assigned to connected computing devices, enabling massivelyparallel simulation of distributed, complex, or functional systems, or acombination thereof.

As a non-limiting example, the properties of entities based on theirfunctional location or attributes can be used to define their behavioras autonomous actors within an agent-based modeling system.

Application: Functional Genomics

In some embodiments, the methods described herein can be applied, asnon-limiting examples, to biological, genomic, proteornic, genetic, orneural systems or databases. A systems syntax can be developed andapplied to functions, attributes, tags, metatags, features, values, orattributes associated with data related to a biological, genetic,genomic, or neural system. As non-limiting examples, a set of genes,chromosomes, neurons, cells, tissues, organs, organ systems, organisms,populations, or ecosystems can be modeled according to the systemssyntax using graphs, networks, coordinates based on the functionalrelationships described herein.

In some embodiments, using the techniques described herein, the capacityto functionally map genomic systems in a way that relates them tobiological systems at higher levels of complexity may enableapplications in gene editing, diagnostics, and predictive analytics.

Application: Functional Relationship Networks

An upper level domain can be based on applications of the functionalinformation system. The upper level domain .locus can be used herein asan example, although any arbitrary combination of allowable characterscould be used as the domain name. The .locus upper-level domain and eachlower-level domain provide user access to a global functional map ofdata entities organized according to the functional locations andfunctional language of a functional information system. Lower-leveldomains can be scoped according to functional identity and can providecontext-based views into the global functional map.

In some embodiments, the .locus upper level domain and each lower leveldomain interfaces with and accesses a syntactic functional databasewhere data entities are tagged, as non-limiting examples, withcoordinates from interrelated and integrated standardizedcoordinated-based tagging systems, including, as non-limiting examples,geographic coordinates and temporal coordinate systems.

The functional relationship network can rely on the identification of acommon anatomy and physiology demarcated through structuring functionalterms based on the techniques described herein rather than an ad hoccollection of natural language terms. The identification of a set ofnatural sequences to the underlying system and the syntacticcodification of common functional roles permits new notions ofconnectivity in the network. In the inventive logical data model, theunderlying set of functions and relationships are common to a pluralityof functional systems regardless of the underlying role of any specificsystem or sub-system thereof.

In some embodiments, a systems syntax for functional information can beapplied to define the web architecture for lower-level domains as theyare instantiated through user accounts and profiles for functionalsystems at various scales. The systems syntax can identify thefunctional identity of a user who creates an account and a profile, suchthat every page in the network will have a functional identity with acommon set of functional relationships to other pages in the system. Asa non-limiting example, the specific function of the user can comprisepart of the domain name for their specific page; in other examples, thefunction and accompanying functional associations are specified on theback-end.

As a non-limiting example, in some embodiments, the platform comprises acommunication system in which a set of functionally identified usersform a network. Within the platform, users can search and navigatethrough the user base to locate other users of interest based onfunctional identity. The platform provides users with tools tofacilitate interaction, including as non-limiting examples, securemessaging, targeted communication, secure financial transaction, andidentity verification. The platform can curate information for usersbased upon functional identity, including data, products, and otherentities of interest to the user.

Users of the platform can self-update identity, which comprisesfunctional and non-functional information, to improve search,navigation, communication, and curated results. The platform candynamically update the users' functional identities based upon userbehavior, including as non-limiting examples communication with otherusers or frequent queries. In some embodiments, an autovicinityalgorithm may use the techniques described herein to define a set ofvicinities of interest for the users based on the outputs of a selectedfunctional proximity algorithm, which can enable the semi-automatedformation of organic communities among users.

Application: Retrodictive and Predictive Analytics in SystemsDevelopment

In some embodiments, the methods described herein may be applied as analgorithmic method for dynamically making predictions for a largedataset representing an underlying functional system, such as:dynamically predicting relationships among elements of an underlyingfunctional system; dynamically predicting outcomes of parts or wholes ofan underlying functional system from the relationships among elements ofan underlying functional system; and dynamically predictingrelationships among elements of an underlying functional system from theoutcomes of parts or wholes of an underlying functional system. Therepresentations can be derived from coordinate or network unification oflinguistic, visual, mathematical, or symbolic representations of thesystem.

The methods described herein can be used to enhance the retrodictive andpredictive capacity of information systems, enabling them to take as aninput a relationship, outcome, or qualitative variable associated withan underlying system and use one or more of the stratified lexicalarchitecture, systems syntax, logical data model, coordinaterepresentation, and graph representation to predict or retrodict anotherrelationship, outcome, or qualitative variable. For example, usinggranular geographic coordinates to study traffic behavior on a specificcorner or intersection in a city, a computer system can predict thetraffic patterns of an entire city transportation system. Conversely,studying a whole city's transportation plan, the system can predicttraffic patterns at a more granular level such as a street corner. Inboth cases, the computer system associates traffic data with fixedgeographic coordinates in order to organize information about activitytaking place at nested levels within the same coordinate system. Mappinggeographic coordinate-based tags to traffic data enables theidentification of specific linkages at specific levels in the system andacross different levels in the complex transportation system.

The same process, linkages, and interrelationships exist incoordinate-based functional systems. If one replaces the transportationsystem described above with a functional system, such as a biologicalcell or an airplane engine, then similar inferences aboutinterrelationships, as well as retrodictions and predictions about thecomposition and outcomes of the functional system at multiple levels ofthe system, can be made. The natural language terms associated with theinternal elements of the functional system can be converted into a setof functional coordinates consisting of one or more interrelated levelsof representation.

Using coordinate-based representations of functional systems,information about functional activity in one part of the system may beused to inform predictions of activity in other parts on the same levelor different levels in the functional system, similar to predictions orretrodictions of activity at one level based on an activity in adifferent part of the same level or different levels of a transportationsystem using geographic coordinate-based representations of the system.In the above example, any type of single or multi-level functionalsystem such as biologic, genomic, genetic, mechanical, structural, fluidor information system can be inserted for the example above that uses afunctional economic system. The capacity to map a system usingcoordinates facilitates prediction and retrodiction acrossrelationships, levels, qualitative variables, and outcomes.

System Architectures

The systems and methods described herein can be implemented in softwareor hardware or any combination thereof. The systems and methodsdescribed herein can be implemented using one or more computing deviceswhich may or may not be physically or logically separate from eachother. The methods may be performed by components arranged as eitheron-premise hardware, on-premise virtual systems, or hosted-privateinstances. Additionally, various aspects of the methods described hereinmay be combined or merged into other functions.

An example computerized system for implementing the invention isillustrated in the figures. A processor or computer system can beconfigured to particularly perform some or all of the method describedherein. In some embodiments, the method can be partially or fullyautomated by one or more computers or processors. The invention may beimplemented using a combination of any of hardware, firmware and/orsoftware. The present invention (or any part(s) or function(s) thereof)may be implemented using hardware, software, firmware, or a combinationthereof and may be implemented in one or more computer systems or otherprocessing systems. In some embodiments, the illustrated system elementscould be combined into a single hardware device or separated intomultiple hardware devices. If multiple hardware devices are used, thehardware devices could be physically located proximate to or remotelyfrom each other. The embodiments of the methods described andillustrated are intended to be illustrative and not to be limiting. Forexample, some or all of the steps of the methods can be combined,rearranged, and/or omitted in different embodiments.

In one exemplary embodiment, the invention may be directed toward one ormore computer systems capable of carrying out the functionalitydescribed herein. Example computing devices may be, but are not limitedto, a personal computer (PC) system running any operating system suchas, but not limited to, Microsoft™ Windows™. However, the invention maynot be limited to these platforms. Instead, the invention may beimplemented on any appropriate computer system running any appropriateoperating system. Other components of the invention, such as, but notlimited to, a computing device, a communications device, mobile phone, atelephony device, a telephone, a personal digital assistant (PDA), apersonal computer (PC), a handheld PC, an interactive television (iTV),a digital video recorder (DVD), client workstations, thin clients, thickclients, proxy servers, network communication servers, remote accessdevices, client computers, server computers, routers, web servers, data,media, audio, video, telephony or streaming technology servers, etc.,may also be implemented using a computing device. Services may beprovided on demand using, e.g., but not limited to, an interactivetelevision (iTV), a video on demand system (VOD), and via a digitalvideo recorder (DVR), or other on demand viewing system.

The system may include one or more processors. The processor(s) may beconnected to a communication infrastructure, such as but not limited to,a communications bus, cross-over bar, or network, etc. The processes andprocessors need not be located at the same physical locations. In otherwords, processes can be executed at one or more geographically distantprocessors, over for example, a LAN or WAN connection. Computing devicesmay include a display interface that may forward graphics, text, andother data from the communication infrastructure for display on adisplay unit.

The computer system may also include, but is not limited to, a mainmemory, random access memory (RAM), and a secondary memory, etc. Thesecondary memory may include, for example, a hard disk drive and/or aremovable storage drive, such as a compact disk drive CD-ROM, etc. Theremovable storage drive may read from and/or write to a removablestorage unit. As may be appreciated, the removable storage unit mayinclude a computer usable storage medium having stored therein computersoftware and/or data. In some embodiments, a machine-accessible mediummay refer to any storage device used for storing data accessible by acomputer. Examples of a machine-accessible medium may include, e.g., butnot limited to: a magnetic hard disk; a floppy disk; an optical disk,like a compact disk read-only memory (CD-ROM) or a digital versatiledisk (DVD); a magnetic tape; and/or a memory chip, etc.

The processor may also include, or be operatively coupled to communicatewith, one or more data storage devices for storing data. Such datastorage devices can include, as non-limiting examples, magnetic disks(including internal hard disks and removable disks), magneto-opticaldisks, optical disks, read-only memory, random access memory, and/orflash storage. Storage devices suitable for tangibly embodying computerprogram instructions and data can also include all forms of non-volatilememory, including, for example, semiconductor memory devices, such asEPROM, EEPROM, and flash memory devices; magnetic disks such as internalhard disks and removable disks; magneto-optical disks; and CD-ROM andDVD-ROM disks. The processor and the memory can be supplemented by, orincorporated in, ASICs (application-specific integrated circuits).

The processing system can be in communication with a computerized datastorage system. The data storage system can include a non-relational orrelational data store, such as a MySQL™ or other relational database.Other physical and logical database types could be used. The data storemay be a database server, such as Microsoft SQL Server™, Oracle™, IBMDB2™, SQLITE™, or any other database software, relational or otherwise.The data store may store the information identifying syntactical tagsand any information required to operate on syntactical tags. In someembodiments, the processing system may use object-oriented programmingand may store data in objects. In these embodiments, the processingsystem may use an object-relational mapper (ORM) to store the dataobjects in a relational database. The systems and methods describedherein can be implemented using any number of physical data models. Inone example embodiment, an RDBMS can be used. In those embodiments,tables in the RDBMS can include columns that represent coordinates. Inthe case of economic systems, data representing companies, products,etc. can be stored in tables in the RDBMS. The tables can havepre-defined relationships between them. The tables can also haveadjuncts associated with the coordinates.

In alternative exemplary embodiments, secondary memory may include othersimilar devices for allowing computer programs or other instructions tobe loaded into computer system. Such devices may include, for example, aremovable storage unit and an interface. Examples of such may include aprogram cartridge and cartridge interface (such as, e.g., but notlimited to, those found in video game devices), a removable memory chip(such as, e.g., but not limited to, an erasable programmable read onlymemory (EPROM), or programmable read only memory (PROM) and associatedsocket, and other removable storage units and interfaces, which mayallow software and data to be transferred from the removable storageunit to computer system.

The computing device may also include an input device such as but notlimited to, a mouse or other pointing device such as a digitizer, and akeyboard or other data entry device (not shown). The computing devicemay also include output devices, such as but not limited to, a display,and a display interface. Computer may include input/output (I/O) devicessuch as but not limited to a communications interface, cable andcommunications path, etc. These devices may include, but are not limitedto, a network interface card, and modems. Communications interface mayallow software and data to be transferred between computer system andexternal devices,

In one or more embodiments, the present embodiments are practiced in theenvironment of a computer network or networks. The network can include aprivate network, or a public network (for example the Internet, asdescribed below), or a combination of both. The network includeshardware, software, or a combination of both.

From a telecommunications-oriented view, the network can be described asa set of hardware nodes interconnected by a communications facility,with one or more processes (hardware, software, or a combinationthereof) functioning at each such node. The processes caninter-communicate and exchange information with one another viacommunication pathways between them using interprocess communicationpathways. On these pathways, appropriate communications protocols areused.

An exemplary computer and/or telecommunications network environment inaccordance with the present embodiments may include node, which includemay hardware, software, or a combination of hardware and software. Thenodes may be interconnected via a communications network. Each node mayinclude one or more processes, executable by processors incorporatedinto the nodes. A single process may be run by multiple processors, ormultiple processes may be run by a single processor, for example.Additionally, each of the nodes may provide an interface point betweennetwork and the outside world, and may incorporate a collection ofsub-networks.

In an exemplary embodiment, the processes may communicate with oneanother through interprocess communication pathways supportingcommunication through any communications protocol. The pathways mayfunction in sequence or in parallel, continuously or intermittently. Thepathways can use any of the communications standards, protocols ortechnologies, described herein with respect to a communications network,in addition to standard parallel instruction sets used by manycomputers.

The nodes may include any entities capable of performing processingfunctions. Examples of such nodes that can be used with the embodimentsinclude computers (such as personal computers, workstations, servers, ormainframes), handheld wireless devices and wireline devices (such aspersonal digital assistants (PDAs), modem cell phones with processingcapability, wireless email devices including BlackBerry' devices),document processing devices (such as scanners, printers, facsimilemachines, or multifunction document machines), or complex entities (suchas local-area networks or wide area networks) to which are connected acollection of processors, as described. For example, in the context ofthe present invention, a node itself can be a wide-area network (WAN), alocal-area network (LAN), a private network (such as a Virtual PrivateNetwork (VPN)), or collection of networks.

Communications between the nodes may be made possible by acommunications network. A node may be connected either continuously orintermittently with communications network. As an example, in thecontext of the present invention, a communications network can be adigital communications infrastructure providing adequate bandwidth andinformation security.

The communications network can include wireline communicationscapability, wireless communications capability, or a combination ofboth, at any frequencies, using any type of standard, protocol ortechnology. In addition, in the present embodiments, the communicationsnetwork can be a private network (for example, a VPN) or a publicnetwork (for example, the Internet).

A non-inclusive list of exemplary wireless protocols and technologiesused by a communications network may include BlueTooth™, general packetradio service (CPRS), cellular digital packet data (CDPD), mobilesolutions platform (MSP), multimedia messaging (MMS), wirelessapplication protocol (WAP), code division multiple access (CDMA), shortmessage service (SMS), wireless markup language (WML), handheld devicemarkup language (HDML), binary runtime environment for wireless (BREW),radio access network (RAN), and packet switched core networks (PS-CN).Also included are various generation wireless technologies. An exemplarynon-inclusive list of primarily wireline protocols and technologies usedby a communications network includes asynchronous transfer mode (ATM),enhanced interior gateway routing protocol (EIGRP), frame relay (FR),high-level data link control (HDLC), Internet control message protocol(ICMP), interior gateway routing protocol (IGRP), internetwork packetexchange (IPX), ISDN, point-to-point protocol (PPP), transmissioncontrol protocol/internet protocol (TCP/IP), routing informationprotocol (RIP) and user datagram protocol (UDP). As skilled persons willrecognize, any other known or anticipated wireless or wireline protocolsand technologies can be used.

Embodiments of the present invention may include apparatuses forperforming the operations herein. An apparatus may be speciallyconstructed for the desired purposes, or it may comprise a generalpurpose device selectively activated or reconfigured by a program storedin the device.

In one or more embodiments, the present embodiments are embodied inmachine-executable instructions. The instructions can be used to cause aprocessing device, for example a general-purpose or special-purposeprocessor, which is programmed with the instructions, to perform thesteps of the present invention. Alternatively, the steps of the presentinvention can be performed by specific hardware components that containhardwired logic for performing the steps, or by any combination ofprogrammed computer components and custom hardware components. Forexample, the present invention can be provided as a computer programproduct, as outlined above. In this environment, the embodiments caninclude a machine-readable medium having instructions stored on it. Theinstructions can be used to program any processor or processors (orother electronic devices) to perform a process or method according tothe present exemplary embodiments. In addition, the present inventioncan also be downloaded and stored on a computer program product. Here,the program can be transferred from a remote computer (e.g., a server)to a requesting computer (e.g., a client) by way of data signalsembodied in a carrier wave or other propagation medium via acommunication link (e.g., a modem or network connection) and ultimatelysuch signals may be stored on the computer systems for subsequentexecution).

The methods can be implemented in a computer program product accessiblefrom a computer-usable or computer-readable storage medium that providesprogram code for use by or in connection with a computer or anyinstruction execution system. A computer-usable or computer-readablestorage medium can be any apparatus that can contain or store theprogram for use by or in connection with the computer or instructionexecution system, apparatus, or device.

A data processing system suitable for storing and/or executing thecorresponding program code can include at least one processor coupleddirectly or indirectly to computerized data storage devices such asmemory elements. Input/output (I/O) devices (including but not limitedto keyboards, displays, pointing devices, etc.) can be coupled to thesystem. Network adapters may also be coupled to the system to enable thedata processing system to become coupled to other data processingsystems or remote printers or storage devices through interveningprivate or public networks. To provide for interaction with a user, thefeatures can be implemented on a computer with a display device, such asan LCD (liquid crystal display), or another type of monitor fordisplaying information to the user, and a keyboard and an input device,such as a mouse or trackball by which the user can provide input to thecomputer.

A computer program can be a set of instructions that can be used,directly or indirectly, in a computer. The systems and methods describedherein can be implemented using programming languages such as Flash™,JAVA™, C++, C, C#, Python, Visual Basic™, JavaScript™ PHP, XML, HTML,etc., or a combination of programming languages, including compiled orinterpreted languages, and can be deployed in any form, including as astand-alone program or as a module, component, subroutine, or other unitsuitable for use in a computing environment. The software can include,but is not limited to, firmware, resident software, microcode, etc.Protocols such as SOAP/HTTP may be used in implementing interfacesbetween programming modules. The components and functionality describedherein may be implemented on any desktop operating system executing in avirtualized or non-virtualized environment, using any programminglanguage suitable for software development, including, but not limitedto, different versions of Microsoft Windows™, Apple™ Mac™, IOS™,Unix™/X-Windows™, Linux™, etc. The system could be implemented using aweb application framework, such as Ruby on Rails.

Suitable processors for the execution of a program of instructionsinclude, but are not limited to, general and special purposemicroprocessors, and the sole processor or one of multiple processors orcores, of any kind of computer. A processor may receive and storeinstructions and data from a computerized data storage device such as aread-only memory, a random access memory, both, or any combination ofthe data storage devices described herein. A processor may include anyprocessing circuitry or control circuitry operative to control theoperations and performance of an electronic device.

The systems, modules, and methods described herein can be implementedusing any combination of software or hardware elements. The systems,modules, and methods described herein can be implemented using one ormore virtual machines operating alone or in combination with one other.Any applicable virtualization solution can be used for encapsulating aphysical computing machine platform into a virtual machine that isexecuted under the control of virtualization software running on ahardware computing platform or host. The virtual machine can have bothvirtual system hardware and guest operating system software.

The systems and methods described herein can be implemented in acomputer system that includes a back-end component, such as a dataserver, or that includes a middleware component, such as an applicationserver or an Internet server, or that includes a front-end component,such as a client computer having a graphical user interface or anInternet browser, or any combination of them. The components of thesystem can be connected by any form or medium of digital datacommunication such as a communication network. Examples of communicationnetworks include, e.g., a LAN, a WAN, and the computers and networksthat form the Internet,

One or more embodiments of the invention may be practiced with othercomputer system configurations, including hand-held devices,microprocessor systems, microprocessor-based or programmable consumerelectronics, minicomputers, mainframe computers, etc. The invention mayalso be practiced in distributed computing environments where tasks areperformed by remote processing devices that are linked through anetwork.

The terms “computer program medium” and “computer readable medium” maybe used to generally refer to media such as but not limited to removablestorage drive, a hard disk installed in hard disk drive. These computerprogram products may provide software to computer system. The inventionmay be directed to such computer program products.

References to “one embodiment,” “an embodiment,” “example embodiment,”“various embodiments,” etc., may indicate that the embodiment(s) of theinvention so described may include a particular feature, structure, orcharacteristic, but not every embodiment necessarily includes theparticular feature, structure, or characteristic. Further, repeated useof the phrase “in one embodiment,” or “in an exemplary embodiment,” donot necessarily refer to the same embodiment, although they may.

In the description and claims, the terms “coupled” and “connected,”along with their derivatives, may be used. It should be understood thatthese terms may be not intended as synonyms for each other. Rather, inparticular embodiments, “connected” may be used to indicate that two ormore elements are in direct physical or electrical contact with eachother. “Coupled” may mean that two or more elements are in directphysical or electrical contact. However, “coupled” may also mean thattwo or more elements are not in direct contact with each other, but yetstill co-operate or interact with each other.

An algorithm may be here, and generally, considered to be aself-consistent sequence of acts or operations leading to a desiredresult. These include physical manipulations of physical quantities.Usually, though not necessarily, these quantities take the form ofelectrical or magnetic signals capable of being stored, transferred,combined, compared, and otherwise manipulated. It has proven convenientat times, principally for reasons of common usage, to refer to thesesignals as bits, values, elements, symbols, characters, terms, numbersor the like. It should be understood, however, that all of these andsimilar terms are to be associated with the appropriate physicalquantities and are merely convenient labels applied to these quantities.

Unless specifically stated otherwise, it may be appreciated thatthroughout the specification terms such as “processing,” “computing,”“calculating,” “determining,” or the like, refer to the action and/orprocesses of a computer or computing system, or similar electroniccomputing device, that manipulate and/or transform data represented asphysical, such as electronic, quantities within the computing system'sregisters and/or memories into other data similarly represented asphysical quantities within the computing system's memories, registers orother such information storage, transmission or display devices.

In a similar manner, the term “processor” may refer to any device orportion of a device that processes electronic data from registers and/ormemory to transform that electronic data into other electronic data thatmay be stored in registers and/or memory. A “computing platform” maycomprise one or more processors. As used herein, “software” processesmay include, for example, software and/or hardware entities that performwork over time, such as tasks, threads, and intelligent agents. Also,each process may refer to multiple processes, for carrying outinstructions in sequence or in parallel, continuously or intermittently.The terms “system” and “method” are used herein interchangeably insofaras the system may embody one or more methods and the methods may beconsidered as a system.

While one or more embodiments of the invention have been described,various alterations, additions, permutations and equivalents thereof areincluded within the scope of the invention.

In the description of embodiments, reference is made to the accompanyingdrawings that form a part hereof, which show by way of illustrationspecific embodiments of the claimed subject matter. It is to beunderstood that other embodiments may be used and that changes oralterations, such as structural changes, may be made. Such embodiments,changes or alterations are not necessarily departures from the scopewith respect to the intended claimed subject matter. While the stepsherein may be presented in a certain order, in some cases the orderingmay be changed so that certain inputs are provided at different times orin a different order without changing the function of the systems andmethods described. The disclosed procedures could also be executed indifferent orders. Additionally, various computations that are hereinneed not be performed in the order disclosed, and other embodimentsusing alternative orderings of the computations could be readilyimplemented. In addition to being reordered, the computations could alsobe decomposed into sub-computations with the same results.

The invention claimed is:
 1. A method for modifying a representation ofa functional system based on functional trajectory signals, the methodcomprising: electronically representing a systems syntax, wherein thesystems syntax comprises a logical data model that can be applied by acomputer processor to evaluate or generate expressions of elements,wherein the elements represent parts, processes, and interactions of afunctional system; electronically receiving an input signal from acomputing device, wherein the signal represents a functional attributeof an element, and storing the input as an attribute of a data entity ata functional location, wherein the data entity characterizes one or moreof the elements; electronically constructing a representation of thefunctional system comprising a graph G by assigning at a set of nodes Nand a set of edges E connected to N to model the functional system attime t₁, wherein N represents the inputs or outputs and E represents thetransformations from inputs to outputs; based on the input signal,algorithmically computing a functional trajectory that assessesmagnitude, distance, or paths among at least two nodes n₁, n₂ from theset of nodes N to infer an outcome in the functional system;constructing in G at least one new edge representing a candidate newtransformation E′ of components from inputs to outputs in the functionalsystem based on the computed functional trajectory; electronicallysending a functional message regarding E′ to a component of thefunctional system; and updating the representation of the functionalsystem to implement the candidate new transformation, the functionaltrajectory representing a set of paths through functional locations overtime.
 2. The method of claim 1 wherein: the input signal is configuredto be represented as a functional location in n-dimensional space, andwherein at least one of the dimensions in the n-dimensional spacerepresents a functional domain, the functional domain comprisingattributes of roles, order, or relationships among the elements; andfurther comprising: electronically assigning a set of functionallocations in the n-dimensional space to the data entity, the locationsbased on attributes of the data entity; and using the relationship ofthe data entity to reference points in the n-dimensional space over timeor movement of the data entity with respect to the reference points asan input to algorithmically computing the functional trajectory.
 3. Themethod of claim 2, further comprising: algorithmically using thefunctional locations in n-dimensional space and the graph representationderived from a systems syntax for predicting changes in composition,structure or location of data entities in n+k-dimensional space or thegraph G; algorithmically computing a functional velocity of the dataentity based on a measurement of a change of the composition, structureor location relative to positions or the reference points at two or morepoints in time; and algorithmically computing a predictive functionalcomposition, structure or location of one or more of the elements in theunderlying system as represented by the data entity in the n-dimensionalspace at a set of specified future times, based on the computedfunctional trajectory and functional velocity.
 4. The method of claim 3,further comprising: taking the integral of the functional trajectory todetermine the functional area; and using the functional area to informthe selection of the candidate new transformation.
 5. The method ofclaim 2, further comprising using massively parallel processing tosimulate the functional trajectory by assigning the set of inputs andoutputs to computing devices and the set of edges to interactions amongthe computing devices; constructing a first coordinate space C ofdimensionality k: k>5 by assigning a set of coordinate values to the setof syntactic tags, wherein the distance amongst the coordinate values ina plurality of dimensions corresponds to the similarity of attributes inthe functional system; electronically inputting data regardingproportions and outcomes in the functional system; and electronicallyassigning an order to the plurality of dimensions based on the extent ofpredictive capacity of similarities of coordinate values forsimilarities of the outcomes in the functional system.
 6. The method ofclaim 1, further comprising: electronically assigning at a set of nodesN′ and a set of edges E″ to model the functional system at time t₂;algorithmically deriving a metric regarding the evolution of one or morecomponents of the functional system based on changes in the graphs fromt₁ to t₂; and using the metric to extrapolate or interpolate dataregarding the functional system at time t₃.
 7. The method of claim 1,further comprising: applying a functional ranking algorithm to thegraph, wherein the functional ranking algorithm assigns a score to aplurality of the components of G by recursively calculating one or morestrengths of the edges and assigning properties relating to functionalattributes of the edges to the connected nodes; and using the functionalranking algorithm to recommend a candidate new transformation E′″ to auser.
 8. The method of claim 7, further comprising using {n₁, n₂}^e asinputs to a computational generative model to algorithmically constructa set of affinity groups A; simulating the performance of a plurality ofaffinity groups a_(1,2 . . . n) εA; applying a discriminative model torank the affinity groups; and modifying the ranking based on a parameterrelated to the user.
 9. The method of claim 7, wherein the functionalranking algorithm is an input to an algorithm assessing affinity amongusers, further comprising; applying an algorithm to assess the diversityof affinity groups and corresponding robustness or resilience to events;applying a simulator tool to assess potential modifications to thesystem and the likely response of the group; and applying a techniqueselected from among agent-based modeling and systems dynamics modelingto determine probabilistically varied time-series paths that may occurwithin a group or in the larger system.
 10. The method of claim 9,further comprising: algorithmically constructing a second coordinatespace C′ by reducing the dimensionality of the coordinate space C tok−x, x≥1, by selecting a subset of the plurality of the dimensions basedon the order; electronically providing a set of visual representationsof proportions of the subset to a user; comparing the set of visualrepresentations to diagnose a phenomenon in the functional system; andwherein reducing the dimensionality decreases the computational searchspace, enabling the set of visual representations to be algorithmicallyprovided to a user based on express or implied preferences.
 11. Themethod of claim 1, further comprising: identifying a subsetC′=c_(1 . . . n−k), k≥1 of the components that are located near theadditional component c_(n+1) in G by using a functional vicinityalgorithm, wherein the functional vicinity algorithm returns a set ofcomponents within a threshold distance score in G based on a distancealgorithm; and engineering an interaction between the additionalcomponent and a component within the subset.
 12. The method of claim 1,wherein the representation of the functional system is associated with acommunication system, further comprising routing a plurality of thefunctional messages based on similarity of components within thefunctional system to direct the functional messages to one or more usersof the functional system.
 13. The method of claim 12, further comprisingmodifying the functional system based on feedback received from theuser; and providing a plurality of search, recommendation, navigation,analytical, data feed, transaction, network, or security modules to auser based on the functional trajectory.
 14. The method of claim 13,further comprising: constructing a community or group of functionalmembers comprising a subgraph g ε G, wherein g comprises n₁, n₂ εN^e₁εE;wherein the community or group is constructed using a functional rankingalgorithm applied to the subgraph g, wherein the functional rankingalgorithm assigns a score to a plurality of the components of g byrecursively calculating one or more strengths of the edges and assigningproperties relating to functional attributes of the edges to theconnected nodes; and wherein the functional community or grouprepresents a plurality of elements sharing a plurality of the functionalattributes; wherein n₁^n₂ represent users; and directing messages tocommunity or group members represented by a plurality of the nodes basedon the strength of edges in the subgraph connecting the community orgroup members.
 15. The method of claim 1, wherein a subset of Grepresents a geographic region, biological system, or grouping offunctional assignments, the functional trajectory represents adevelopmental path for the geographic region, biological system, orgrouping of functional assignments; and the functional velocitycorrelates to a growth rate, further comprising; taking the derivativeof the functional velocity one or more times to derive a higher-orderderivative of the functional trajectory, and using the higher-orderderivative to extrapolate or interpolate a metric or outcome in thefunctional system; and using the velocity or higher-order derivative asan input to computing the candidate new transformation.
 16. The methodof claim 1, wherein N+E₁>10,000, and wherein a set of locations in S areassigned based on a word embedding algorithm in hyperdimensional spaceof dimension d so that semantic meanings are rendered as tensors orvectors, further comprising: constructing a tensor space or vector spaceof dimension l≤d+t+s based on the output of the word embeddingalgorithm, temporal data in dimension t, and geographic data indimension s; assigning a set of functional markers to a plurality of theelements {g_(1,2 . . . n)}εG; wherein the functional markers areselected from a semantic, visual, auditory or audiovisual tag applied toa set of functional data, and the functional markers associatefunctional data, relationships, and a signifier; wherein theidentification of functional markers enables the provision of aninterface to a set of users to access search, recommendation, ornavigation results; assigning a rank to a plurality of functionalmessages based on their algorithmic distance in l or the similarity oftheir functional markers; and sending the functional message to a userbased on the rank and the properties of the user.
 17. The method ofclaim 1, wherein the functional system is biological or genetic; andwherein the candidate transformation represents agricultural traitmodification and intervening in the system comprises using precisiongene editing to increase crop yields, disease resistance, or weatherresistance.
 18. The method of claim 1, where the functional system iseconomic, financial, monetary, or fiscal, further comprising:algorithmically simulating a plurality of outcomes related to thecomputed functional trajectories; and ranking the plurality of outcomesand associating the ranked outcomes with candidate new transformations.19. The method of claim 1, further comprising algorithmicallyidentifying unique phenotypes to the elements based on functionallocations and levels of expressions; computing a set of metrics andoutcomes associated with unique phenotypes; and using unique phenotypesto recombine, synthesize, or reengineer the elements to improve outcomesin the functional system.
 20. The method of claim 1, further comprising:storing a computerized representation of a system S with elementsE={e_(i)}, i=1, 2 . . . n, wherein S is comprised of subsystemss_(1,2 . . . j), with each s_(i) having a set of elements ε_(i) ⊂E,${{\overset{k}{\bigcup\limits_{1}}ɛ_{i}} = E},$ wherein each e_(i) hascharacteristic properties p_(1, 2 . . . i),${{\overset{l}{\bigcup\limits_{1}}p_{i}} = P},$ related to its inputs,outputs, or operations in S; constructing a set of expressionsX={x_(i)}, wherein each x_(i) is comprised of a combination of two ormore elements ε_(i) sharing a property p_(i), ∃s_(i): x_(i)⊃s_(i)∀x_(i)∈X; storing a population Z with data entities D={d₁},wherein Z is comprised of subpopulations z_(1, 2 . . . j), with eachz_(j) having a set of data entities Δ⊂D,${{\overset{k}{\bigcup\limits_{1}}\Delta_{i}} = D},$ with attributes A;wherein the collection of subpopulations z_(1, 2 . . . j) determines thestructure of Z; constructing a set of composites C={c_(i)}, wherein eachc_(i) is comprised of a combination of two or more data entities Δ_(i)sharing an attribute a_(i), ∃z_(i): c_(i)⊃z_(i)∀z_(i)∈Z; and enabling adata creating, reading, updating, and deleting operation on the dataentities.
 21. The method of claim 20, further comprising: associating aset of numerical values V={v_(i)} with two or more subpopulations z_(i)and two or more composites c_(i); associating a set of statisticalproperties W={w_(i)} among z_(i) and c_(i); and ordering z_(i) and c_(i)such that w_(c)>w_(z).
 22. The method of claim 21, wherein: f: S→Z, g:E→D, and h: P→A are surjective; and e: X→C is surjective.
 23. Anelectronic computing system for enabling a modification of a functionalsystem based on a computation of functional trajectory, the systemcomprising: an electronic computing device configured for storing anelectronic representation of a systems syntax, wherein the systemssyntax comprises a logical data model that can be applied by a computerprocessor to evaluate or generate expressions of elements, wherein theelements represent parts, processes, and interactions of an underlyingsystem; the electronic computing device further configured for storing:an electronic input from a computing device, wherein the data entitiesat a functional location characterize one or more of the elements, andstoring the input as a data entity; a graph G comprising a set of nodesN and a set of edges E assigned to model the functional system at timet₁, wherein N represents the inputs or outputs and E represents thetransformations from inputs to outputs; an algorithmic computation offunctional trajectory that assesses magnitude, distance, or paths amongat least two nodes n₁,n₂ from the set of nodes N to infer an outcome inthe functional system; an output of computing the functional trajectoryto inform the electronic construction in G; at least one new edgerepresenting a candidate new transformation E′ of components from inputsto outputs in the functional system; a signal regarding E′ sent to acomponent of the functional system; and the electronic computing devicefurther configured for computing an update in the representation of thefunctional system to implement the candidate new transformation andstoring the update in the electronic computing device configured forstoring, the trajectory representing a set of paths through functionallocations over time across the universe of elements E.
 24. Theelectronic computing system of claim 23, the electronic computing systemfurther comprising: a collection of subsystems {s_(j)}⊂P(E), whereinevery element is in at least one subsystem; a universe of properties P;and a function for associating elements with properties f: E→P(P)wherein the function is surjective.
 25. The electronic computing systemof claim 24, wherein a plurality of N represents labor in the functionalsystem and the signal indicates potential job training, skilldevelopment, job application, recruiting, job placement, hiring,staffing, promotions, or labor policy, further comprising: an inclusionfunction for associating subsystems comprising members of {s_(j)} withtheir elements such that f: {s_(j)}→E; wherein Z comprises: a universeof data entities D; a collection of subpopulations {z_(j)}⊃P(D); auniverse of attributes A; a function for associating data entities withattributes g: D→P(A) a map carrying; {s_(j)}↔{z_(j)}, P↔A; a simulationfunction assigning a probability distribution K to a set of outcomesassociated with a plurality of z_(j); and a map ϕ: D→E that associates aset of data entities with a set of elements of the system.
 26. Theelectronic computing system of claim 25, further comprising: anelectronic set of nodes N′, and a set of edges E″ that model thefunctional system at time t₂; an algorithmically derived metricregarding the evolution of one or more components of the functionalsystem based on changes in the graphs from t₁ to t₂; and anextrapolation or interpolation of data based on the algorithmicallyderived metric regarding the functional system at time t₃.
 27. Theelectronic computing system of claim 26, further comprising: afunctional ranking algorithm applied to the graph, wherein thefunctional ranking algorithm assigns a score to a plurality of thecomponents of G by recursively assessing the strength of the edges andimputing certain properties of the edges to the nodes they connect; anda recommendation to a user of a candidate new transformation E″ based onthe functional transformation.